All right everybody, welcome back. It's Veronica Howard. So this time around we're going to be talking about generalization. We're going to go through a very basic example of what generalization is. We're also going to be talking a little bit about applications of generalization. How do you actually foster some generalization? And we're going to finish up talking about those advanced clinical applications or times when generalization goes wrong. We'll also be talking a little bit about the basic research and some studies on generalization. But first, when we're trying to figure out what generalization is, we need to know what generalization isn't. So let's return to some of our previous content. Remember that discrimination training is all about narrowing the range of stimuli that a person will respond to. The formal definition of discrimination training, it's a procedure in which behavior is reinforced in the presence of one stimulus and extinguished in the presence of many other stimuli. So to translate this to English, we're teaching people where and when and with whom to emit the response and very often that behavior will only be reinforced in a very narrow range of circumstances. It will not be reinforced in others. An example of this would be, for instance, if I were to ask you, what's the stimulus on the left? What is this one over here? Now in the presence of that stimulus on the left, there's only one naming response that will contact reinforcement. That's Apple. In the presence of the stimulus on the right, if I were to say what's this and you were to say Apple, you would not contact reinforcement. So in this particular case, that one stimulus, in the presence of that stimulus, one response and one response only will be reinforced. In the presence of other stimuli, that same response will not contact reinforcement. In this case, that Apple is the SD. For the response to Apple, the orange is the S Delta. It will not be reinforced in the presence of that behavior. Apple will not be reinforced in the presence of that stimulus. Generalization, however, is exactly the opposite. The point of generalization is that the behavior is reinforced when it occurs in the presence of lots of stimuli. And often we see generalization as a phenomenon takes place when a behavior that we have trained under different circumstances occurs in a novel or new circumstance. We also have to understand what a stimulus class is. A stimulus class or stimuli that are related along some dimension, the color or the shape or some quality that they have in common. And remember a novel stimulus is a new stimulus. It's something that our learner has never seen before. So let's go back to our Apple orange example. In the presence of this stimulus, if I were to say what's this, right, this Apple is an SD for the response, Apple. And if you emit that response, you'll contact the reinforcer. But what if I present you with this new shape, this new item you've never seen before? Well, what's this? And if you emit that same response, Apple, you'll contact reinforcement. So in this case, remember, this will contact reinforcement. But what happens when we present someone with this new stimulus and they give us no response? Well, in this case, generalization has not occurred because they have not emitted the same response, Apple, in the presence of this green fruit.  In mainstream general psychology, we would talk about this idea of a stimulus class. Now, these stimuli that I'm showing you on screen now all share a common feature. They're all part of the concept of Apple. And a concept is a mental grouping of similar objects or items. They have something in common. But remember that behavior analysts typically don't talk in terms of mental groupings because that assumes some sort of private event. We don't like to think in that language. And so rather than relying on a kind of mental construct to explain this, we talk about behavior in terms of stimulus classes. And a stimulus class is a set of stimuli that are related along some dimension that there's stimuli that have some common feature or property. So for instance, when I show you these flowers and this Pantone color and this fruit, they'll have something in common. They all share the common quality of being items that are the color orange. Or if I were to show you again the same fruit, and I were to show you this fruit, and I were to show you this fruit, they all share the common feature of being part of the citrus family. They all descended from three major basic citrus. They all share a kind of acidic quality. And the stimulus classes don't have to be simple like this. They can be a little bit more abstract. So for instance, if I were to show you this lemon, and I were to show you this aspirin, and I were to show you vinegar, they all share something in common. All of these items are acidic and all of them, because of their acidic nature, are used in cleaning or they can share some common features they could be used to dissolve certain items if you took them long enough. So stimulus classes can be topographical. They can focus on the form of an item. They can also focus on other characteristics like the function or what they do. What matters is those stimulus classes develop through experience. It's our previous history that tells us whether a stimulus falls into that class or doesn't fall into that class. Now this would ordinarily be the point in a face-to-face course where I actually talk about folks learning history with them. And you may be familiar with a couple of years ago. There was this big fervor. There was a big conversation about this song. It's outdated. It's outmoded now, but it's a song called Old Town Road. If you're not familiar with it, check out the optional reading. Essentially, the long story short of this particular song was that it became very, very popular on some radio stations. It started on TikTok and then moved to radio stations. People were requesting it. And it started climbing the charts on the Billboard Top 100 for country music. But then suddenly the song disappeared. And it was unclear why the song was removed from the country Billboard charts. Some folks said, well, it had to do with the qualities of the song itself. It had to do with the fact that there's a kind of underlying rap-esque or urban quality to it. And others looked at the fact that the song was removed from the country music charts as being evidence of a kind of a systemic racism. The idea that the person who had created this particular song was a black artist. And people thought, well, the reason it was removed from the charts was because you can't have a black artist on the country music charts. The question that we're asking here is, does this song as a stimulus deserve to be in the same stimulus class as other kinds of country music songs? So I might invite you here to take a moment, stop the video, and define what are the qualities that make country music country? What is it that country music has to have that it embodies that concept or that stimulus class of country? Is it a particular sound? Is it a particular type of artist? Is it a particular sort of format? Are there certain instruments that have to be present or must be absent? Does it have to have a particular type of narrative? For instance, do they have to talk about particular themes or tropes? What is it that makes country country? And does the song Old Town Road, remember there's a link to it in the description and in your study guide, does that song fit into the stimulus class of country? Why are we not? What's interesting about the scenario is it kind of embodies for us this idea of a generalization gradient. Now, when we're talking about generalization, we're talking about whether or not we respond in the same way to a novel stimuli as we do to ones we've been trained to in the past. And you can actually visually chart our probability of responding on this thing called a generalization gradient. The generalization gradient is a graph. It's a visual demonstration of the probability that we will respond to a novel stimulus based on the features that it shares with the stimulus that we have been trained to. So in this case, we're talking about probability indicated on the y-axis and along the x-axis. It's showing you how similar is the stimulus that you're being presented with to the stimulus you've been trained to. So this is kind of like a match to sample. How similar is this to the thing that you were trained to that's in the center? And as that stimulus changes slightly, in this case, we're talking about wavelengths of a noise. As that noise gets a little bit higher in pitch or a little bit lower in pitch, we may be less likely to select it. And then the more different it is, the less likely we are to select those stimulus features. I can give you another example. Let's imagine that we have a scenario here where our discriminative stimulus is an apple and we present different fruit. We might say, where are we likely to present? What are we likely to say? Shares those stimulus properties with the apple. And in this case, maybe you're trained on the red apple. And I present you with a green apple and you have maybe an 80% likelihood of selecting. Yeah, that's the same. I'll select that. And then I present you with an orange and you're 50-50 on that. Then I show you a banana and you're really unlikely to select that. And all the way down here on the right, I show you a chicken and ain't nobody going to say that a chicken is the same as an apple. So this is a visual demonstration of the probability that we're going to select a stimulus that's similar to the one that we've been trained to. It kind of shows us whether we're going to respond to a novel stimulus in the same way. Another way of looking at a generalization gradient could be, for instance, this. So if you've been trained to this kind of teal color in the middle, this shows you graphically the probability that you would endorse that the colors, these other colors, are that same color. So if I train you to the teal, you're very likely to select this kind of off-green color just to the right of it, but much less likely to say that orange is the same color as teal. Now generalization is a very basic feature of all animal behavior. For the most part, we need to have generalization. We need to have this in our repertoire. Like could you imagine a world in which we had to learn new skills in every single new environment that we went to? We would not be very adaptable creatures. So on some level, we generalize because this works for us because we are able to take our behavioral repertoires into new vistas, into new places, and actually contact reinforcement. We might see that our ancestors who had a repertoire that was able to generalize were those that were more successful in branching out from their homes and finding new places to live and contacting food and resources. So on some level, generalization allows us to work in settings or with people that we've never experienced before. It allows us to be very robust and adaptable, but that doesn't mean that generalization is always good. We can in fact over generalize. So for instance, if we're talking about the consumption of certain beverages, there are certain liquids that we would potentially consume that have a kind of light yellow color that wouldn't necessarily be bad. But there are also other liquids that have a kind of light yellow color that if we consume them, we would not enjoy the flavor. We might even get sick from it. So we see that discrimination, being able to tell the difference between the liquid on the left and the liquid on the right, that's a valuable repertoire as well. So remember that generalization is not always beneficial. You can have a phenomenon known as over generalization. And over generalization is where the behavior occurs in the presence of a novel stimulus where it will not be reinforced or potentially even punished. Okay, so remember that we talked about discrimination training. It's where we're trying to narrow the range of stimuli that a learner will respond to. We want them to respond in the presence of only a few stimuli, whereas generalization is exactly the opposite. We want to widen the range of stimuli people will respond to. We want to increase the range of stimuli where people are going to respond and give us that response so we can reinforce it. So it's just a question of, do you want to teach people to tell the difference between, or do you want to increase the likelihood that people are going to emit that response in the presence of new stimuli? Then you select your training procedure based on your goals. In discrimination training, we reinforce only in the presence of a narrow range of stimuli. And in generalization training, we reinforce in the presence of lots of different stimuli. So we're going to come next time and talk about generalization training. I'll see you guys next time.


Hello, in the last few lectures we have been talking about low pass filters. In the low pass filter we discussed about different types of filter realizations such as Butterworth, Chebyshev, Bessel filter and Elliptic filters. We saw how to find G parameters for these different Butterworth and Chebyshev filter. For Butterworth expression for G parameters was very very simple. However, for Chebyshev we have to first define how much ripple we want in the pass band and as I mentioned please do not design for ripples more than 0.5 dB in the pass band because more than 0.5 dB ripples in the pass band will lead to very poor VSWR in the pass band region. And we had also seen that for a faster transition from the pass band to stop band where we had taken the design example of omega 1 divided by omega c equal to 1.2 where we wanted attenuation of 30 dB. We saw that a Butterworth filter would require a 19th order filter whereas, a Chebyshev with the ripple in the pass band of 1 dB would require only 8th order filter. So, you can see that if you use Chebyshev filter you can reduce the number of components. So, we noted that for the Chebyshev filter the order required was only 8th order whereas, for Butterworth the order required was 19th. So, that means, you will require 8 LC components for the Chebyshev filter and 19 LC components for Butterworth filter. So, depending upon the requirement one should do the design accordingly. So, we had also seen that instead of realizing these filters using lumped elements like inductors and capacitors we can also use microstrip lines. We had earlier seen a small transmission line of length less than lambda by 4. If it is shorted it realizes inductor and if it is open circuited it realizes capacitor. So, we had used that concept to design low pass filter. Now, let us look into how we can do the transformation from low pass filter to high pass filter or band pass filter or band stop filter. In fact, we had seen in the previous lecture that a transfer function of a low pass filter is given by this particular expression. And since we know that high pass filter is nothing, but in words of low pass filter all we have to do it is in this S over here which we have designated as capital S over here. If we change this S to 1 by S then we can realize a high pass filter and we had seen very quick example let us just go through it quickly. So, if you put S equal to 1 by S 1 by S over here. So, that is the high pass filter expression for band pass filter what we have to do we have to transfer low pass filter which was from 0 to normalize value of 1 to a band pass filter with the center frequency of omega 0 and band width equal to b. So, all we have to do it is shift this one to the central position where center frequency is equal to omega 0. So, we use the transformation that is S we use this particular expression S square plus omega 0 square divided by B S. So, that is the transfer function of band pass filter and the transfer function of band stop filter can be obtained by knowing the fact that band stop is nothing, but in words of band pass filter. So, we use the inversion of this one here which is B S divided by S square plus omega 0 square and we get the transfer function of band stop filter. Now, comes the next part how do we design these filter? Since we have already found out the G parameters for low pass filter we can use this concept of frequency transformation to design high pass filter, band pass filter and band stop filter. So, let us see how we can do that.  So, for low pass filter wherever we have a inductor that inductor is to be replaced by capacitor why? We had seen that for the impedance Z is equal to SL and S has to be replaced by 1 by S and we know that for a capacitance Z is equal to 1 over SC. So, that is how we can actually find out the value of the capacitance. So, we can find the value of the capacitance by using this particular expression or I will show you in the next slide how to use the G parameters itself to find the new values of the high pass filter component. So, inductor becomes capacitor, capacitor becomes inductor for band pass filter wherever there is an inductor that is to be replaced by series L and C and wherever there is a capacitor it is to be replaced by parallel LC combination. For band stop filter inductor has to be replaced by parallel combination of inductor and capacitor and a capacitor has to be replaced by series combination of inductor and capacitor. As you can see again from band pass filter to band stop you have to do you can say the cross of this. So, this is because of the reason that band stop filter is nothing, but inverse of band pass filter. Let us just see now one by one how to realize these components for different filters. So, for low pass filter to high pass filter transformation what we need to do? Let us first look at the low pass filter circuit configuration. So, what you do for the design let us say we want to design a Butterworth high pass filter. So, the first step would be actually speaking you design a Butterworth low pass filter. Similarly, suppose you have to design a chubby shape filter of let us say ripple 0.5 dB in the pass band. So, what you do first you design a low pass filter find all the G parameters. So, G 1, G 2, G 3, G 4 and so on. So, now as I mentioned earlier so, inductor is to be replaced by capacitor, capacitor is to be replaced by inductor. Now, you do not have to find G parameters again these G parameters which are here G 1, G 2, G 3 and you can see that instead of writing here small G's we have written here capital C and capital L. So, here for these particular things all you need to do it is for low pass filter to high pass filter transformation. So, capital G K which is of course, again G K's happens to be my initials also Girish Kumar. So, capital G K can be obtained by simply equal to 1 divided by G K. So, this small G K's are corresponding values of G parameters. So, for example, C K dash is nothing, but equal to 1 by G 1 this will be 1 by G 2, 1 by G 3 and so on. And after that once you know what is C K which is equal to 1 by G 1 simply use that impedance, frequency scaling transformation to obtain the values of C. Let us see how now we can do the thing from low pass filter to band pass filter. Again what you do? You have to design let us say a Butterworth band pass filter. So, you design a Butterworth low pass filter or you want to design a Chebyshev band pass filter then you design first Chebyshev low pass filter find all the G parameters. So, G 1, G 2, G 3, G 4 not this G 1 which I have actually represented here as capital L K, but this inductor has to be replaced by combination of inductor and capacitor. So, do not get confused this L K dash does not mean inductor and capacitor, but actually speaking this is simply representation of this over here ok. So, inductor has to be replaced by series inductor and capacitor and the capacitor over here which has been now termed as C K that capacitance corresponding to this number here is to be replaced by parallel combination. So, how does this really happen? How this G 1 which is inductor gets transformed to series component? So, for that let us just see what we had done for the transformation from low pass filter to band pass filter we had used the expression that S was transformed to this particular expression. Now, for inductor we know that what is that Z is equal to S times G 1 because here G 1 represents inductor. So, now substitute the value of S by this particular expression which is the transformation from low pass filter to band pass filter. Now, simplify this here we can see that there is a S square in the numerator and in the denominator we have S. So, separate this out this will become S G 1 divided by B and if you look at the plus term after that the next term is omega 0 square divided by B S G 1. Now, for impedance we can represent these terms as series combination of inductor and capacitor. Inductor is defined as S L whereas, a capacitance is defined as 1 by S C. So, if we now compare this equation with this here we can say that L is nothing, but equal to G 1 by B and what is C equal to you can see that 1 by S C. So, S is here. So, C will be B divided by omega 0 square multiplied by G 1 ok. So, this is how you can find the values of L and C. So, now let us see we have to transfer the capacitance into this particular combination here for that I suggest that you do these steps yourself, but to do that step let me just give you little bit of a hint that for capacitance you can write instead of Z write Y. So, Y is equal to S multiplied by G 2. So, over here then S will become this particular term and this will be G 2 remember now this is Y and in Y if we have to add the two components they will be in shunt ok. So, that is how these two comes in parallel or we can say these two are in shunt then only they are added ok. So, this process is similar. So, you follow the same thing for inductors and capacitor for all these components and that way you can find out the corresponding values of L C components for band pass filter. Now, for band reject filter I leave that exercise for you people to do it. So, we know that band reject filter is nothing, but inverse of band pass filter. So, simply use the inverse of this particular transformation simplify in this particular manner you can find out the components of band reject filter. So, now let us just take an example. So, this is a third order Butterworth band pass filter which we took as an objective to be designed at 100 megahertz because that is easy then to transfer to any other frequency. So, the first step is that you actually design a third order low pass filter ok at 100 megahertz or you can actually speaking design it for the normalized frequency omega equal to 1. So, the first step would be that you design a third order low pass filter at normalized frequency omega equal to 1 and here just to show you what we have here. So, think about a low pass filter would be a capacitor that inductor capacitor and now you just look at the transformation inductor was replaced by series combination of inductor and capacitor. A capacitor what was supposed to be here is now replaced by parallel combination of inductor and capacitor it is just shown slightly different way you can see here this is ground this is ground. So, had we drawn this particular thing on this side this capacitor will be over here and this capacitance will be over here. So, capacitance in case of low pass filter is replaced by inductor in parallel with capacitance inductor in case of low pass filter is replaced by series inductor and capacitor and the capacitor for low pass filter is replaced by inductor in parallel with capacitance. And now for the transformation we have used the bandwidth as 20 megahertz . Now I just want to tell you that whatever those design value comes out to be they are not practically available in the market ok. So, what we have done we have actually chosen L and C values which are practically available and these values are chosen close to what were the designed values. So, you can see here these are the values which are relatively available in the market. So, you can see here this is 27 nano henry 100 pico ferrate 8.2 pico ferrate. So, this is 313 nano henry inductor and these values are same as these value over here. Now these are readily available component values. However, when you take these values as we will see in the next slide the center frequency does not remain precisely 100 megahertz, but we will see what are the shift. Now this particular thing has to be now fabricated. So, we have actually designed a general purpose PCB and I just want to mention to you that this general PCB we had designed for low pass filter, band pass filter, band reject filter, attenuators also which we will discuss in the later lectures. So, let us see what we have done here. So, here this is the input port this is the output port and the width of this particular line must be chosen corresponding to 50 ohm characteristic impedance. So, you can see here corresponding to this point here a SMA connector has been connected here the center of that pin is soldered over here for the output. You can see that at the output SMA connector is connected. So, now what you see over here these are the basically pads where we can put the components. Now what we have here you can see at the bottom side there are several plated through holes ok. So, basically these are done to provide proper grounding from the top to the bottom same thing has been done over here also. Now multiple plated through holes have been taken the reason for that is if we just put only let us say one plated through hole over here then shorting happens at this particular point whereas, if we are going to put a component over here it will see the path length something like this and that path length may provide additional inductor ok. So, this is a general purpose thing and now you can see from here how we have done the realization. So, you can see here from here there is an inductor. So, this inductor is realized by this air core inductor over here. In fact, this kind of a thing can be very easily realized all you do it is take one of those transformer windings and what we have done over here is that just take the refill of the ball pen and wrap it around that and then of course, you have to do little bit of a calculation to find out the desired value of the inductor. However, as I also mentioned that these inductor values are readily available you can also purchase a lumped equivalent of this particular thing here and that can be soldered between this particular point over here to this particular point over here ok. And then the capacitor can be soldered between this and this and you can do a shorting over here ok and then you can keep following this particular thing. So, we have a capacitance over here you can see there is a capacitance and since it is a large inductor again this large inductor has been realized using a air core inductor, but again you can buy a chip inductor also. So, that is the air core inductor then after that we need a inductor which is going to ground we need a capacitance which is going to ground. So, that is going to ground and whatever things you do not need to use simply put a copper strip and solder that particular portion. So, let us see now what we got. So, first let us see the simulated results now these simulated results are not for the designed value these simulated results are for the available component values. So, you can see here this is the plot for as you can see from here dot purple line here is for S 2 1. So, this is the S 2 1 simulated I want to bring to your attention even though we had designed 400 megahertz, but because of the available component values the simulated values shifted slightly, but since this was just for testing the concept it is ok. So, it is fine we can do that let us see corresponding to this particular simulated S 1 1. So, S 1 1 is shown by blue color. So, this is the S 1 1 plot you can see that most of the time it is less than minus 15 dB in the desired passband, but when we did the fabrication. So, you can see that there is a little bit of a shift in the resonance frequency. So, this is the S 2 1 measured. So, you can see that this is the measured plot one can actually see that there is a small shift in the resonance frequency and also there is a small shift in the measured S 1 1 value also. So, why there is a shift because the reason for that is that even though when we buy these readily available components they do not have 0 percent tolerance majority of these components have 5 percent to 10 percent tolerance. So, because of those component tolerances resonance frequency can change. Another thing I want to mention that we had taken those finite lengths in between which were acting as pad for these component. So, that also provides series inductor or maybe parasitic capacitance. So, because of that also generally speaking resonance frequency decreases slightly. So, when you have to design your next band pass filter or low pass filter remember that you have to take some of these precautions that all those line lengths do have parasitic inductance and capacitance and invariably they try to reduce the designed resonance frequency slightly. So, please take care of these things when you actually do the design. Now, you can see here that lot of inductors capacitors are required and then component tolerances and other things play very important role. So, now we look into some of the designs where you do not need inductors and capacitors, but use simply transmission line or modifications of transmission line to realize various filters. So, let us look at these things now. So, here 3 different configurations are shown over here. So, let me go through these things one by one. So, this is a end coupled band pass filter and this is generally designed when the bandwidth required is less than 5 percent. I just want to mention here what is percentage bandwidth. Percentage bandwidth is defined by bandwidth divided by center frequency multiplied by 100 ok. So, end coupled filters are generally designed for narrow bandwidth which is less than 5 percent. So, what is this configuration here and why these are known as end coupled. So, I just want to tell you. So, each one of these things here are approximately lambda by 2 resonators. So, these resonators will act like a band pass filter we know that a lambda by 2 resonator will actually speaking have a band pass filter response like this ok. And when you use multiple of these band pass filter section basically what happens if you use only one section the transition from the pass band to the stop band will be relatively slow, but if you use larger number of these resonators then basically what happens we can will have a sharper transition from the pass band to the stop band. So, since these resonators are coupled at the end that is why these are known as end coupled band pass filter. Now, just I want to mention here that if you want to increase the bandwidth why there is a problem the problem is that this cap here especially the gap between the first element and the last element becomes extremely small. In fact, this gap may become even of the order of 0.1 mm or sometimes even smaller and you know that if you want to realize a 0.1 mm and you go for a PCB fabrication there are chances that 0.1 mm gap may not be there and the two things will get shorted ok. So, that is why generally speaking end couples are used only for smaller bandwidth. However, to increase the coupling the next step is we use coupled line band pass filter and generally these are designed for 5 percent to 20 percent bandwidth. So, here let us see what we have again these are lambda by 2 resonators somewhat similar to this concept over here, but now instead of end coupled like this they are coupled like this. When we are talked about the coupled line microstrip and we had also talked about coupled line directional coupler I had mentioned to you that the coupling is maximum between the resonators when this length is equal to lambda by 4. So, you can see that the total length is lambda by 2. So, this lambda by 4 is coupled with this lambda by 4. So, that becomes one coupled line configuration this becomes another coupled line configuration this becomes another coupled line configuration and by using this particular configuration what we are doing we are increasing the coupling between the input port and the next element and then similarly we keep on increasing the coupling and by increasing the coupling we are able to increase the bandwidth from 5 percent to 20 percent. However, there are applications where we need bandwidth for more than 20 percent. So, in that particular case we can use the concept of direct coupled. So, let us see what it is. So, you can see here this one here shows only one section of course, you can see here there are three sections over here there are multiple sections over here right now let me explain you the concept with the single section. So, here this length is lambda by 4 which is shorter to ground. Now think about the transmission line theory. So, transmission line theory if you recall. So, if there is a lambda by 4 length then the input impedance becomes Z 0 square divided by Z L. So, if Z L is equal to 0 which is shorter to ground what will happen over here it will become open circuit. So, that means corresponding to this particular length where it is lambda by 4. So, that particular frequency when we give input here this will act as a open circuit. So, everything go from here to there at other frequencies loading of this short will come over here and that will get attenuated. As I mentioned this is only a single section multiple sections can be realized using this particular configuration here. So, you can see here this is input this is output and we have several lambda by 4 sections over here. So, you can see here 1, 2, 3, 4 and in between each lambda by 4 section we have another lambda by 4 transformer in between ok. So, these things generally are designed for sharp roll off and for wider bandwidth requirement. Of course, just to mention here instead of using a shorted lambda by 4 section you can also use open ended lambda by 2 section also. So, in case of open ended lambda by 2 section what will happen this length will be let us say lambda by 2 and we know that for lambda by 2 section transmission line whatever is the load impedance will become source impedance. So, in this case load impedance is open. So, source impedance will become open. So, if these things are open circuited whatever is the input that will go to the output at other frequencies these things will provide attenuation to the signal. So, let us see now how we can realize a band reject filter we have to just remember the concept that band reject is nothing, but opposite of band pass filter. So, I have just shown the direct coupled concept here for other configuration you can actually try to visualize yourself. So, here we have again a lambda by 4 section, but now this particular end is open circuited. Since this is lambda by 4 this open will act as a short over here ok and if it is short. So, whatever the input is given at that particular frequency it will get shorted. So, that will not go over here. So, basically it will act as a band reject filter at a frequency where this length is equal to lambda by 4. Now, instead of having a length like this you can always use a bent length also and the same thing can be done even for band pass filter. Now here depending upon how close is this bent ok. Suppose you make a bent very very close to it and the length is let us say lambda by 4 then there will be two modes of coupling. One coupling will be of course, direct coupling like this here other coupling can be because of the fringing fields especially if this length is very very close to this here. So, you can basically increase the coupling and also you can make the filter instead of this width you can now make it relatively compact. So, we will look at a one design example and let us see then what kind of a results we get. In fact, I have given a title slightly different here it is a band pass filter and band reject filter depending on a length. The reason will be clear in a few minutes. So, let us see what we have done here. So, we have used a low cost FR 4 substrate these are the substrate parameters and what we have chosen here line width which is 1.5 mm here for the 50 ohm line and this is a lambda by 4 resonator width of that has been taken as 0.5 mm. In the next lecture I will show you what is the effect of changing this particular width, but right now just to tell you we took this length of the line as 42 mm. Let us see the frequency response of this particular configuration. So, we are giving a input here this is the output all we have here is a open circuited line which is of length 42 mm. So, see here this is frequency and this is the S parameter response. So, let us just look at the green color which shows S 2 1. So, for S 2 1 I have written here band pass filter when L is equal to lambda by 2 I have written here band reject filter when L is equal to lambda by 4 or when L is equal to 3 lambda by 4. So, let us see what are these things ok. So, let us just think about this is an open circuit. So, this open circuit will act as a short circuit at this particular point when this length is equal to lambda by 4. So, if this open here acts as a short circuit that will become like a band reject filter. So, this is the response corresponding to when length is equal to lambda by 4. You can quickly check now frequency is approximately equal to 1 gigahertz. So, at 1 gigahertz wavelength is 30 centimeter lambda by 4 will be 30 divided by 4 which is 7.5 centimeter or you can say 75 mm. Now, 75 mm is to be divided by square root of epsilon effective of this particular line not this line ok because this is acting as a resonator. Since the line is very thin its epsilon effective is also relatively small you can see that this is epsilon r 4.4 epsilon effective will be much smaller than 4.4. So, 75 mm is divided by this epsilon effective which actually gives to the length of 42 mm. So, when this length is lambda by 4 it acts like a band reject filter because this is open will act as a short. When this length is lambda by 2 and when this length will become lambda by 2 when the frequency is doubled which is approximately 2 gigahertz. So, at 2 gigahertz length becomes lambda by 2. So, open becomes open over here when the length is 3 lambda by 4 what happens now open over here will act as a short circuit.  So, you can actually see that this particular simple thing here can act as a band reject filter or band pass filter or band reject filter depending upon the frequency of operation and you can see the corresponding S 11 plot. So, when band pass filter characteristic is satisfied that means, everything is going from here to here that means, nothing is reflected back. So, reflection coefficient is very small. In case of band reject filter nothing is going over here. So, almost everything is reflected back. So, you can see that S 11 is very high at this particular point. So, we will continue from here in the next lecture we will take more examples of how to realize these band pass filters and band reject filter. So, thank you very much we will see you next time. Bye.


in this presentation we will take a look at tests of details transactions related to the accounts payable cycle so the accounts payable cycle test of details transactions looking at the assertion of completeness assertion of completion first a word from our sponsor well actually these are just items that we picked from the youtube shopping affiliate program but that's actually good for you because these aren't things that were just given to us from some large corporation which we don't even use in exchange for us selling them to you these are things that we actually researched purchase and use ourselves acer 27 inch monitor i've been using an acer monitor as my primary monitor for a few years now this is the first acer monitor that i have used after having used a series of different brands of monitors in the past the acer monitor has been performing well and i'm trusting the acer brand more and more as i use the monitor i have a 27 inch monitor which i think is ideal for what i do which is of course the screen recording and the editing if you would like a commercial free experience consider subscribing to our website at accounting instruction dot com or accounting instruction dot think of it dot com where we have many different courses you can purchase one at a time or have a subscription model giving you access to all the courses courses which are well organized have other resources like excel files and pdf files to download and no commercials the auditors auditors should conduct a search of unrecorded liabilities that include the following so completeness of course being that assertion that we want to make sure that everything that should have been recorded is recorded in other words are the end results done in the financial statements is everything on the financial statements are they complete in other words are there transactions that have happened that are not reflected in the financial statements in the end result so how do we test for this inquire management about control activities designed to identify unrecorded liabilities and accruals at the end of the accounting period the controls would be part of the closing process uh vouch large dollar items from the purchases journal and cash disbursements journal for a period of time after year end now remember what we have here is after year end because we're doing the audit as of uh the the let's say 1231 the year in let's say 1231 of course we are doing the audit at some point after that point in time so if we're testing something we can actually take a look at some of the transactions that happened after uh the year has closed and use them as part of our testing process examine the data on each receiving report of vendor invoice to see if the liability relates to the current audit period so we're going to take the information and we're going to look at the data that would should be used in order to determine when something should be recorded in this case that being the receiving report why because the receiving reports usually going to be that item before talking about purchases that we actually received the item so we want to see if that's the point in time that the item was actually put on the books was it put on the books in the correct time period it should be put on the books in accordance with the receiving reports we want to see what's the triggering factor as to when the item is going to be put on the books in the accounting system and then basically double check those and we can do that by looking at some of the transactions after the end of the time period and checking to see if it has indeed been recorded at the time period it should have that being the time period the receiving report uh happened we want to examine files of unmatched purchase orders receiving reports and vendor invoices for in any unrecorded liabilities next assertion related to test of details of transactions is existence with existence auditors primary worry is whether the recorded liabilities are valid obligations of the entity so the recorded liability on the books are they valid liabilities of the entity now again you would think that with regards to liabilities they wouldn't overstate the the liabilities but that's basically what we're testing for it with regards to existence because you would think if they were overstating liabilities they wouldn't typically do that intentionally it might be an error possibly to overstate the liabilities but you would think that you wouldn't intentionally overstate the liabilities usually because that would make you look worse the only time that that might happen generally is if there's something for tax reasons or something like that but typically we would think that if there was going to be some type of intentional misstatement they would usually be trying to look better now not worse orders should vouch a sample of items on the listing of accounts payable to the supporting documentation so we're going to take the information from the end result then existence we're talking about here and then we're going to vouch it back to the source documentation and that'll help us to be able to see if the end result was on the books actually it happened so we're going to take the end result and then go back to the past next we have the assertion with relation to the test of details of the cutoff so recall that the cutoff is typically going to be that year-end type of information are things properly recorded in the proper time period order order will try to determine if all purchase transactions are recorded in the correct period for most audits the purchase cutoff line line up with the entity's physical inventory count so we're going to basically line this up when we're going to do it with the physical inventory count and that will typically happen somewhere close to basically the year-end so that we could be so we can check that the physical inventory was on the books as we go out and check the physical inventory is indeed present at that point in time proper cutoff should also be determined for purchase return transactions so we also want to consider the cutoff with regards to purchase returns next we'll take a look at test of details transactions with regards to rights and obligations the assertion of rights and obligations the risk is small related to this assertion because entities generally do not have an incentive to record liabilities do not that are not obligations of the entity so usually when we're considering the rights and obligations with regards to liabilities again the assertion normally the company wouldn't try to look worse most of the time and therefore it's not an assertion that's as high of a priority with regards to liabilities typically next we're going to take a look at the assertion of accuracy valuation and allocation accounts payable should be recorded at either the gross amount of the invoice or net of the cash disbursement amount valuation of accruals depends on the type and nature of the accrued expenses most accruals are fairly easy to value next we'll take a look at the assertion of classification the primary issues with regards to classifications with the test of details of transactions are find and reclassify any material uh debits contained in accounts payable so we're going to go through the accounts payable the detail of accounts payable if there are debit balances in the accounts payable balances then it shouldn't be the case that we would should have a debit balance in accounts payable something kind of funny possibly happened at that point in time and we'd want to remove any debit balances in the accounts payable now there could be an accounts a debit balance if there is some kind of policy so for example if we purchase something and we typically put like a down payment on the purchase of something before we receive it it could be possible that the system then has has been set up that we put that into a negative payable meaning we would kind of have a negative payable to the to the vendor why would we do that because the accounting system makes it a little bit easier to do it could make it a little bit easier to track by vendor what is owed to the vendor instead of putting it into into basically an advanced an advanced payment so instead of putting it into an asset in other words of an advanced payment before we receive the the goods whether it would be inventory or some other type of asset we put it in as a negative liability because it's going to match up once we received the goods that we were going to receive and the system will make it a little bit easier for us to do that with regards to the matching up process of the vendors so if we if that is the case and we would probably want to inquire to the organization to see if that's going to be something they do within their normal policy we may well have debit balances in the in the accounts payable accounts and then we're just going to reclassify them from debit you know negative balances of a liability to asset balances and then we have separate short-term and long-term payables we want to make sure that we're separating out the short-term and the long-term payables make sure that different types of payables are properly classified so we have different types of classifications payables we want to make sure that they are in those proper classifications next we're going to take a look at the assertion of presentation there are two disclosure items of primary importance for accounts payable and accrued expenses with regards to presentation auditor needs to make sure that all related party purchase transactions have been identified so remember whenever we have this related party transactions we could think of a related party such as a subsidiary or something like that then we have a we have issues because we're not we're concerned that there's not an arms length transaction we don't have market forces to help us determine that the transaction is at basically market prices therefore we want to identify those for sure and look into those types of transactions if material the related party purchase transactions should be disclosed so if the related party purchase transactions are material material component we want to disclose those because again that relationship kind of makes those transactions a bit suspect in terms of whether they're market validity of those types of transactions the other primary concern is purchase commitments when the entity has entered into a formal long-term purchase contracts proper disclosure of the terms of the contract should be provided as a footnote so when we have long-term basically contracts we want to make sure that we're clear on what the commitment is in the contract if we have a very complex contract and it's we're dealing with something that's going to be material that's a problem we want to know exactly where we stand in terms of the long-term obligations of a contract now we're going to take a look at accounts payable confirmations now when you think of confirmations you're you're thinking about a third party verification and normally if you hear confirmation the first thing that pops into your mind is probably accounts receivable confirmations that's where we are most likely to do confirmations that and the bank you know we'll send confirmations to the bank we'll send confirmations to accounts receivable most of the time some of the customers to confirm the balances owed to the entity by customers counts payable we can do the same thing but it's usually not as necessary a process so we're almost definitely going to do it for the cash some type of confirmation we're probably going to do it for accounts payable at least to some degree depending on the entity we're doing and then accounts payable we may do it but it's a lesser degree of likelihood that we'll do confirmations meaning we're going to send confirmations out basically to the vendors now that owe the company I mean that the company owes money to the company that we are auditing owes money to the vendors so they're going to be used less often than accounts receivable confirmations partially because auditor is able to examine externally created source documents related to accounts payable so notice in accounts payable we have other type of source documents that are not generated from inside the organization as opposed to accounts accounts payable when we're looking at the things that generated the accounts payable the source documents are generated by the company so that's going to be less reliable type of information if we just look at the invoice that's going to be less reliable information with regards to accounts payable we're looking at bills and things that are going to be given from outside of the organization therefore they are more reliable and possibly then we can rely less on things like confirmation when confirmations are used they are usually positive and are generally blank confirmations in other words notice what we're not doing here we're not saying we're not saying hey here is the balance and you tell us basically yes or no on it or we're not we're not even saying here's the balance and you know don't send it back if you don't agree with it which would be a negative to confirmation we're having a positive confirmation saying hey we would like you to send it back either way and they don't really have the option because we're going to send it blank meaning we're not going to say here's the balance and do you agree with it or not we're going to say you know we feel that this company that we are auditing owes you this much money as of this date or owes you money as of this date would you confirm the balance we're not going to give the balance we're going to give it blank they're going to show us the balance as of that date now notice that even a lot of times when we think about these confirmations from the accounts receivable side of things notice the person that receives it if you're talking about receivable confirmations the person that receives it is owing the company that we're confirming the money and therefore they're they have less incentive to be kind of cooperative there they might see the thing and say and and not want to deal with it or say that I don't owe the company money at this point in time however if you're if you're dealing with a vendor typically that means that the company that we are auditing owes them money so if we ask them do we owe you money they're more they're more likely to know exactly what that is and maybe have incentive to look it up and check it out and send it back to us so they're more they might be more likely and more incentivized to actually to have a higher rate of return of the confirmations in other words to accounts payable people because they're the people that the company that we're auditing owe money to and we're asking them how much money the company that we are auditing owe them and so they might be more likely to take it back now also remember all the rules with the confirmations are pretty much you know the same here we the auditor are doing the confirmation we're not going to do it on the company letterhead we're doing it outside of the company we're going to send them directly to the vendors and then the vendor is going to send them directly back to us the audit firm not to the company so we're keeping the company out of it the vendor is asked to provide the balance owed by the entity so then we have the audit findings identify misstatements with will be aggregated so we're going to take the misstatements we're going to aggregate them we're going to have the projected misstatement is then compared to the tolerable misstatement so the projected misstatement that we get from our findings we compare to the tolerable misstatement the level of misstatement that we accept that would be acceptable that we're going to basically accept if it's and then if the projected misstatement is less than the tolerable misstatement the auditor has evidence that the account is fairly presented so then we're going to say okay if it's less fairly presented however if the projected misstatement is greater than the tolerable misstatement the auditor will conclude that the account is not fairly presented so if it's greater than the tolerable misstatement then of course we'd have to conclude it's not fairly stated


a fiery horse with a speed of light, a cloud of dust, and a hearty hyoseilver! The Lone Ranger! With his faithful Indian companion, Tottle, the daring and resourceful masked rider of the planes led the fight for law and order in the early western United States. Nowhere in the pages of history can one find a greater champion of justice. Return with us now to those thrilling days of yesteryear. From out of the past come the thundering hoofbeats of the Great Horse Silver! The Lone Ranger rides again! Canyon City was made up of a few stores, the main office of the Damon stagecoach company, and a hotel a cater to travelers who had to wait some time several days for accommodations on the stagecoach. Jake Parker ran the hotel and spent most of his time behind the counter in the lobby. He was there when Jim Blake entered and slapped dust from his well-worn clothing. I guess you don't remember me, do you, Mr. Parker?  Now let me think. I spent the night here in your hotel one year ago. Name's Jim Blake. From your clothes I'd say you'd been prospecting in the hills. Yeah, you're right. Any luck? Well, Freda Midland, I spent most of my time panning streams and hit some good ones. Glad to hear it. You aim to stay in town? I guess so. How long does it take for the stage to get from here to Carsonville and back? Well, it used to take two days in each direction. What do you mean it used to? Well, sometimes it takes longer now. Spent some Indian trouble. Puyoots have attacked a few of Damon's stages. Puyoots? Well, I thought they were peaceful. Didn't they sign a treaty? A treaty? I'd have attacked one of the stage coaches three times the last few months. Is that so? It's got so Damon won't be responsible for shipments that are lost. So if you're figuring on sending your gold to the bank in Carsonville, you better think again. I can't carry it around with me, especially with so many owl hoots in town. What do you mean so many owl hoots? Crooks, gunslingers, men with their guns tied low. Those two gents sitting over in the corner, for example, I'd bet anything they'd live by their guns. And I saw lots of others just like him in the street. As long as any man can pay for what he buys in my hotel, I don't ask questions. Now, I've got to get my gold to the bank in Carsonville. It's the only safe place. I hope it gets to Carsonville. I'll ride with it to make sure. How soon does the next stage leave? Find that out from Damon. His office is at the far end of the street. Yes, Mr. Blake, it's quite true we have had some trouble with Puyoots. In spite of the peace treaty they signed? I wouldn't say that Puyoots is a whole of broken the treaty, but a band of them has been making it hot for my stage line. Well, I wanted to send some gold to the bank in Carsonville. I'll weigh it and give you a receipt. But in the event of Indian attack, of course, I cannot be responsible. I'm going to go with it. As a passenger on the stage court? Yeah. Well, that's up to you. You have to pay full fare. I'll pay. In that case, you might as well carry the gold with you. There's no use having me take charge of it. Well, you have a strong box on the stage, haven't you? Well, that might give me a little more protection. Stage leaving this afternoon. Good. Here's the dust. You'll have to weigh it. Stage will leave at three o'clock. I'll be here. A few minutes after Jim Blake left the office of the stage coach company, Jake Parker came in to call on Damon. Oh, hi, Jake. Glad you came. I have something to discuss with you. Sorry, young prospect, your name Blake, leave here. He's shipping gold on this afternoon stage. Damn, I should work. Over $5,000? Worth going after him. Yes, he's sending it at his own risk. He's going to ride the stage himself to keep an eye on the gold.  Tell them to get rigged out as payouts and watch for the stage coach. Well? What's the matter? Damon, I've been wondering. We don't want to overwork that payout Indian business. Well, we may hear about it and come to see about the Indians breaking the treaty. What are but who can prove it's not the payouts that stick up my stagecoaches. Couldn't the boys do it without dressing up like payouts? I want a guard and driver, as well as any passengers who might be on board to describe the attackers as Indians. That throws suspicion off our own boys. I think the guard and driver should be in on the deal. Just that many more to pay off. God might shoot one of our own men. Lefty and the other boys know they must take that risk. Furthermore, I've warned the guard to avoid starting gunplay that would lead to his own death, as well as the death of the driver and passengers. Don't tell me how to run my business. I'm not, I just wouldn't. You just take care of the hideout and the costumes, Jake. I'll do the rest. It was later that same afternoon when the stage left Canyon City to head for Carsonville, with gold belonging to Jim Blake and several other men. The horses followed the familiar trail through the hills for over an hour. Jim Blake and another passenger were inside the stagecoach, and the guard and driver rode on top. Suddenly, an Indian war cry rang out through the hills. Hey, yeah! It seemed like a fire. Hey, guys, read in. Open fire. Those red skins are firing at us. They shoot down our heads.  There, the guard is right. They're robbers. They're the robbers anyway. You won't save your cash for dying. The guard and driver stuck their hands into the air, as a small body of men in war paint, wearing a clothing of pious Indians, rolling past us around the Hothick stage. The attackers worked quickly, and with the efficiency of a well-drilled team, they dragged the guard and driver from the box, and the passengers from inside the stage and took away all weapons. Then they smashed the strong box, loaded the contents into saddlebags, and rode away. There goes every cent I have in the world, all my gold dust. There goes a solid year of hard work. Yeah, we're lucky to be alive. You, God, why didn't you fight? Why didn't you let me shoot them? That wouldn't have helped any, Mr. Blake. We might have drilled one or two, but the others would have killed us in short order. And Mr. Damon told us not to risk flies by shooting. But why doesn't the government step in? Why do they let those Indians break a treaty like this? Hey, look over there. Coming from all the direction. War Indians. Just one Indian. And others are... He's a mess. Yeah, more robbers. Well, at any rate, there's nothing left for them to steal. Just two of them. We could get them if those pilots hadn't taken our guns. Let's get in the stage and make a run for it. Well, you think my team could outrun those two horses? Another chance. May as well stay right here until those critters they came too late. Oh, no, no, no, no, no, no, no, no. They're too late, Mr. They've already been cleaned out. The pilot's robbed us. Well, anyone hurt? No, but I'd soon have a bullet in the shoulder and lose all it was stolen. You may as well shove on, I'll hope. We got nothing left to steal. You're jumping to the wrong conclusion. We came to investigate the gunfire and offer help. You'd say Paiute Indian hold up stage? That's right. Where'd they go? That way, toward Canyon City. Yeah, and if you'd have been here a minute earlier, you'd have seen them riding over yonder hills. Sooner we get back to town, the sooner the marshal can get a posse out to hunt them. Mind if we get a boy at the stage and get going? Searchers, if you don't believe we've been robbed. Be fast so we can get started for time. I don't want to search you. You mean we're free to go? You really do think I'm an outlaw, don't you? It is a big flop. I'll tell Mr. Damon the stage is coming back. You'll tell. You mean you're going to town? We may see more of each other. Ready, Tuttle? Be ready. Come on, Tuttle! Let's go! A long ranger and Tuttle reached the edge of town without catching sight of the men who had attacked the stage. They found a suitable campsite in a woods, where Tuttle waited while the masked man rode to the rear of a row of buildings. But he left his horse and entered Simon Damon's office. Damon's face registered surprise. Who are you? My name wouldn't mean anything to you, Damon. I wear this mask because there are men who would shoot me on sight if they recognized me. Oh, what do you want? First of all, I want your confidence. It'll help if you've heard of me. I'm called the Lone Ranger. What? You, the Lone Ranger? Why, I can't believe that. I can show you a silver bullet and my horse is in back. You might recognize silver from descriptions. Other than that, I don't know how I can prove my identity. In any event, please listen to me. Yes, yes, I'll listen to you. Have been reports that Paiute Indians have attacked your stagecoaches. That's true. Maybe true that your coaches have been attacked, but it was not the work of Paiute. I... how do you know? Because I've investigated. I came here directly from the Paiute village toward the east. Those Indians have a lot of respect for the peace treaty they signed. They're proud of their status as law-abiding people. They would put to death any of their tribe would display any form of violence. But I have eyewitness reports. Passengers who are on the stagecoaches, as well as my garden driver. It would not be hard for white men to disguise themselves as Paiutes.  No, more than that. Your stage was attacked this afternoon between here and Carsonville. It was. My statement will be confirmed within an hour when the stage returns. The men who attacked it looked like Paiutes, but they came directly here. See, how do you know that? Their trail was fresh. Todd and I could follow it to the heart ground within a half mile of town. But not into town, eh? Several of the horses had distinguishing hoof marks. We may be able to identify them. See, well, now, what you say is very, very interesting, but have you given this information to the Marshal? Not yet, but I shall. Unless you prefer to pass it on to him yourself. Well, I'll be glad to. These crooks must be found and exposed before the Paiute Indians are involved in serious trouble that might result in the breaking of the treaty. Yes, I'll speak to the Marshal just as soon as possible. He'll probably want to question you. I'm sure he'll want to meet you. Todd and I are camped in a clump of cotton which was directly south of town. The Marshal can find us there. I'll tell him. Meanwhile, we'll be looking for the horses with the distinctive hoof marks. Oh, wait, I'd like to talk to you some more. We'll probably meet again. Hmm, a lone ranger, eh? That's bad. Come on, do it! I must do something about him. You alone, Cameron? Oh, come in, Jake. Come in. You're just the man I want to see. Oh, there's the back door, all right. I've all checked in, turned over the goal, they got from Blake. Jake, listen to me.  He knows it isn't Pio to attack the state's coaches, and he's likely to find out the truth about our game. We've got to get rid of him before he gets us. Now, me man. No, he's not in uniform. A laman? He's not wearing a badge. Well, who in turn is he?  The curtain falls on the first act of our lone ranger adventure. Before the next exciting scenes, please permit us to pause for just a few moments. Now, to continue. When the lone ranger told the owner of the stage line that the highwaymen were not Pio Indians, he didn't realize that Damon himself was the leader of the gang. Nor did he suspect that Jake Parker, owner of the hotel, was Damon's right-hand man. The two conspirators knew that their security had to be bought by the murder of the lone ranger. Tuttle had gone to town to scout for information, and the masked man was alone in camp when a horseman approached.  Hi there, missy. Hello. I reckon you're the man I'm looking for. They told me you were camped in these trees. Steady boy. I've been expecting someone who'd come to ask questions.  Are you from the Marshal's office? Oh, yeah. Hey, see, will you sell your horse and come back to town with me? Marshal wants to talk to me. Very well. You used to be silver. Well, you've done some water on that fire while I settled my horse. Right. So you're the lone ranger, huh? Yes. You can call me lefty. You said you came from the Marshal's office. Oh, yeah. I don't have a badge. I'm not a regular lawman. Just running an errand for the Marshal. Oh. He sent me because he wants me to show you something on the way back to town. What are you to show me? Well, it's a cave in the hillside. Marshal wants you to look it over and see if you've got any ideas about it. Yeah, I'm ready. All right, lead the way. Right. Get up there. Come to the lefty. Lefty rode in the direction of town and approached a hill in the rear of the hotel. He drew rain and they dismounted. Near a dense stand of underbrush at the bottom of the hill, it concealed the entrance to a cave. Yeah, follow me. I'll show you how to get through the brush. Right. Hey, now you can see the opening. Goes right straight into the hill. Dark inside. Got a bit of candle in my pocket. Light it as soon as we're inside. We can dodge around some big boulders. This cave goes straight through the hill, slanting down with a little bit, about 50 yards long. Well, there, now you can see. A tunnel? Yep, it's what it is, a tunnel. And the other end opens into the cellar of the hotel. You follow me. As the lone ranger followed lefty through the tunnel, three men appeared from behind the brushwood at the mouth of the cave. I'd like to follow along and see what happens.  What better doing, sirs? Well, I ain't aiming to go against Jake's orders. Just the same, I'd like to be in the hotel cellar when the lone ranger learns that Damon is our boss. That'll be worth seeing, man. Now, there, you can see the end of the tunnel is a wooden door. It opens into the hotel cellar. Well, what are we going to find there? We're going to find proof that what you told Mr. Damon is right. Those highwaymen weren't Paiutes at all. They were white men. The hotel cellars are hard-eyed, and that's where they keep their engine clothing. I'll see if the door's open. All right, there's a light in there. Yeah, so I see. Open the door a little while. Step right in, Mr. Paiutes. What's going on? I'm holding a gun on your back. The boys are waiting for you. Get your hands up and come in here. Damon. Come in and meet Jake Parker, who owns the hotel, and the boys who rob the stage from. Holding his hands at shoulder level, the lone ranger took two steps into the room, then moved slightly to one side while left they came out of the tunnel. The masked man saw a large room with walls of stone. A flight of stairs at one end led up to a door that probably opened into the first floor of the hotel. In addition to Damon and Jake Parker, a half a dozen hard-faced men eyed the newcomer. Piled on a nearby table, there lay buckskin jackets and trousers, as well as headdresses typical of Paiute Indians. I seem to have played right into your hands. Damon. Locked yourself for death when you came into my office with the guests that the robbers were white men dressed as Paiutes. Hey, Lefty, where's the Indian? Indian? But I said this masked man has an Indian pal named Tonto. Told you to bring him both. I didn't see nothing of a red skin in his camp. We've got to have Tonto. We won't be safe until both he and the lone ranger are dead. You're right about that, Damon. Tonto has just as determined as I had to clear the name of the Paiute Indians.   You won't get Tonto. You're not even sure of me. With lightning speed, the lone ranger leaves behind Lefty, snacks the gun, and fires two shots toward the lamp. Get him. Stop him. Where is he? Get a light. His sudden move caught the others completely off guard. He was in the tunnel and slammed the door. Quiet down now. Quiet all of you. Take it easy. He can't get away. The boys are watching me outside of the tunnel. All right, Pete, get a light. Joe, open the door. Two can play at that game. Can't see him in the tunnel. He'll be able to see us when we get a light. Stand out of the line of fire. What about that light? I got another lamp up there, dude. Hey, boys. You at the outside, can you hear me? The masked man got away. He's heading toward your end of the tunnel. Don't let him out. The tunnel was studded with big boulders. The lone ranger ran into several of them as he hurried through the darkness. He heard Damon shouting to the men outside near the horses and knew that he was trapped.  He pelted between two rocks, which gave him temporary protection. Some bullets fired at either end of the long tunnel. But he knew that his security would be short-lived. He's trapped, boys. He can't get away. How are we going to get him? He could shoot us if we went into the tunnel after him. We're not taking that chance.  I didn't see him at camp. Wait for him. Bring him back here. We can use him to bring that masked man out of the tunnel. While Damon's men watched both ends of the tunnel, Lefty went up the cellar stairs to the hotel. He borrowed one of the horses at the hitch rail and rode over the hill to the tunnel's entrance, where he had left his own horse beside Silver. Ho! Ho! There! Ho! Ho! Easy now. I keep a sharp watch, boys.  Where are you going, Lefty? I'm taking my horse and I'm going to get the lone rangers in the impale. Steady now.  As Lefty approached the lone rangers' camp, he saw a fire burning far brighter than the one he had extinguished earlier that evening. Hold it. Hold it. Hold it. As he rode into the camp, he saw no sign of Tonto. The Indian appeared from behind a tree as the outlaw dismounted. Easy there.  You've got your cupboard. Take it easy, Tano. I'm from the marshals' office. Well, what you want? I was here a little while ago to get your friend. He's with the marshals right now, helping Sal the stagecoach robberies. You hear of four? Sure, that's what I'm telling you.  I don't mean no, you tell truth about lone rangers. I'd have no reason to lie. Oh, you've got plenty reason to lie. Now get hands up. All right, hold on. Now listen, Tano. I'll see here the marshals ain't gonna like this. The marshals not like it. When I'm here, you hold up stage. What do you mean? You ride without law. Oh, you talk. Dangerous.  That's not true. Somehow, you got the idea. One of the outlaws now. That's crazy, Tano. Be fine marks of outlaw horse. One horse got broken shoe. Same horse here in camp a little while ago and same horse here now. So that's it, huh? Well, if you think you can... Now, you talk. Now, wait a minute. Listen to me. I borrowed that horse. I don't know... Where are lone rangers? Are you talking? No. Talk fast. Don't beat me. Don't beat me like that. Red skin. Do not talk. Damon, Jake and the other thieves have maintained a constant vigil in the cellar room while others in the gang did the same thing at the outer end of the cave. Meanwhile, the lone ranger was trapped between the two. It was nearly midnight when the door opened and Tano appeared at the top of the cellar stairs. An Indian. Me, Teller, man lefty, say you want me. Yep, that's right, Tano. Come on down here. Him say, mask friend here. You'll be with your mask friend in just a few minutes, Tano. I'll get your hands up. Here, come on. Take his guns, boys. Get ropes on him. Now we'll get that mask man. Hey, you, back there in the cave. We've got your Indian pal. You want to come out peaceful or stay there and listen to him howling pain from what we do to him? Me not howling pain. Get him roped and be quick about it. You hear me? I heard you. So did I. Marshall. Let him have it. Bedlam broke loose when the Marshall leaked down the entire flight of stairs with other lawmen at his heels. Damon and his men went for their guns but fired too fast. Their shots went wild. Then the Marshall's men went into action at close range. Tano jerked free and swung a hard fist at the nearest man. It was a hand-to-hand fight at quarters too close for further gunplay. The lone ranger could hear the action. He knew what had met and rushed from the tunnel into the room to add his way to the forces of law. This is for you, Damon. The fight was quickly ended. Damon and Jake were bruised and beaten and their men were in even worse condition. Line up there against that wall. Hold on, Marshall. There's a mistake. There was a mistake, Damon, and you made it when you tried to beat the law. That goes for you too, Jake. I got the whole truth from Lefty. Tano brought him into my office and he spilled all he knows including the fact that all the gold that's been stolen from the stagecoaches is in a chest right here in this room. Oh, that squealing double-crossing. Don't hold it too much against Lefty. You'd a squeal too if Tano'd gone to work on you the way he did on Lefty. Good for you, Tano. He'd make big mistake when he'd ride horse with broken shoe. That reminds me. Silver's on the far side of the hill. There are others at the gang. We went there first and brought in those crooks.  He's there waiting for you. Good enough. Come along, Tano. You want that cash, Blake? I'd hear my children. Then that cleans everything up. Gosh, my children. If it hadn't been for that masked man, I'd have lost all I got in the world. I'll sure be everlastingly grateful to him. And to Tano. Jim, you're not the first to say that about the masked man. I guess you already know who he is. Yeah, I sure do. He's the Lone Ranger. This is a feature of the Lone Ranger Incorporated, created by George W. Trendle, produced by Trendle Campbell Enterprises, and directed by Charles D. Livingston. Tonight's drama was written by Franz Breiker. The part of the Lone Ranger is played by Brace Beemer.