Hello, and welcome to this presentation of the STM32 Analog-to-Digital converter block. It will cover the main features of this block, which is used to convert the external analog voltage-like sensor outputs to digital values for further processing in the digital domain. The Analog-to-Digital converter inside the STM32G0 microcontroller allows the microcontroller to accept an analog value, like from a sensor output, and convert the signal for use in the digital domain. There are up to 19 Analog inputs. The ADC module itself is a 12-bit successive approximation converter with additional oversampling hardware. The oversampling unit pre-processes the data to offload the main processor. It can handle multiple conversions and average them into a single data with an increased data width up to 16 bits. The sampling speed is 2.5 mega-samples per second for 12-bit resolution. The data can be made available either through DMA movement or interrupts. This ADC is designed for low power and high performance. There are a number of triggering mechanisms and the data management can be configured to minimize the CPU workload. The ADC module also integrates an Analog watchdog. The input channel is connected to up to 19 channels capable of converting signals in either single-end or differential mode. The ADCs can convert signals at 2.5 mega-samples per second in 12-bit mode. There are several functional modes which will be explained later. There are also several different triggering methods. In order to offload the CPU, the ADC has an Analog watchdog for monitoring thresholds. The ADC also offers oversampling to extend the number of bits presented in the final conversion value. For power-sensitive applications, the ADC offers a number of low power features. This slide shows the general block diagram of the ADC. The left part describes the Analog front-end based on the Analog multiplexer and the embedded sampling capacitor of the ADC. This sampling time must be enough for the input voltage source to charge the sample and hold capacitor to the input voltage level. The right part is the digital back-end. Samples are stored into a data register that's either read by software or transferred to memory via a DMA channel. Three Analog watchdogs monitor the voltage of selected Analog input with regard to high and low thresholds. When the voltage is not within the guard range, an interrupt may be generated and a trigger event may be signalled to the timer units. Note that the Analog front-end can be power-gated when the ADC is not used and also between acquisitions by using the auto-off function. The ADC supports a deep power down mode. When the ADC is not used, it can be disconnected by a power switch to further reduce the leakage current. When weight mode is active, the ADC's wait until the last conversion data is read or the end of conversion flag is cleared before starting the next conversion. This avoids unnecessary conversions and thus reduces power consumption. The ADC has an automatic power management feature which is called auto-off mode. When auto-off mode is enabled, the ADC is always powered off when not converting and automatically wakes up when a conversion is started by a software or by a hardware trigger. A start-up time is automatically inserted between the trigger event which starts the conversion and the sampling time of the ADC. The ADC is then automatically disabled once the sequence of conversions is complete. Auto-off mode can be combined with the wait mode conversion for applications clocked at low frequency. This combination can provide significant power savings if the ADC is automatically powered off during the wait phase and restarted as soon as the ADCDR register is read by the application. The power consumption is in function of the sampling frequency. For low sampling rates, the current consumption is reduced almost proportionately. The ADC includes the oversampling hardware which accumulates data and then divides without CPU help. The oversampler can accommodate from two to 256 time samples and right shift from one to eight binary digits. The sequencer allows the user to convert either up to 19 channels in ascending or descending order or up to 8 channels in a user-defined order. Two sampling periods can be programmed. Each channel is assigned one of these two values. The ADC offers a self-calibration mechanism for the offset. It's recommended to run the offset calibration on the application if the reference voltage changes more than 10%, so this would include emerging from reset or from a low power state where the analog voltage supply has been removed and reinstated. High temperature excursion may also require to run the offset calibration. The ADC needs a minimum of 1.5 clock cycles for the sampling and 12.5 clock cycles for conversion for 12-bit mode. With a 35 MHz ADC clock it can achieve 2.5 MHz per second. For a higher sampling speed it's possible to reduce the resolution down to 10, 8 or 6 bits. The sampling times listed in this slide in ADC clock cycles are available. Longer sample times ensure that signals having a higher impedance are correctly converted. At a given time, only a pair of possible sampling times is active. For each analog channel, the user is free to select one of these two selected values. The ADC has a selectable clock source. When the system needs to run synchronously, the APB clock source is the best selection. If a slow CPU speed is required but the ADC needs a higher sampling rate, the dedicated ADC clock can be selected. In this case the ADC implements 2 clock domains, P clock and ADC clock and delays are needed to perform the re-synchronization between them. The ADC supports several conversion modes. Single mode which converts only one channel in single shot or continuous mode. Scan mode which converts a complete set of predefined programmed input channels in single shot or continuous mode. This continuous mode converts only a single channel at each trigger signal from the list of predefined programmed input channels. The ADCs support hardware over sampling. They can sample by two to 256 times without CPU support. The converted data is accumulated in a register and the output can be processed by the data shifter and the truncator. This functionality can be used as an averaging function or for data rate reduction and signal-to-noise ratio improvement as well as for basic filtering. Each ADC has three integrated 12-bit analog watchdogs with high and low threshold settings. The ADC conversion value is compared to this window threshold. If the result exceeds the threshold, an interrupt or timer trigger signal can be asserted without CPU intervention. The ADC conversion result is stored in a 16-bit data register. The system can use CPU polling, interrupts or the DMA controller to make use of the conversion data. An overrun flag can be generated if data is not read before the next conversion data is ready. In case of overrun, either the new sample is dropped or the previous sample is overwritten. Each ADC can generate eight different interrupts, ADC ready, end of conversion, end of sequence, end of calibration, analog watchdog, end of sampling, data overrun and channel configuration ready. DMA requests can be generated at each end of conversion when the ADC output data is ready. The ADCs are active in run and sleep modes. In stop mode, the ADCs are not available but the contents of their registers are kept. In standby mode, the ADCs are powered down and must be re-initialized when returning to a higher power state. There's a deep power down mode in each ADC itself which reduces leakage by turning off an on-chip power switch. This is the recommended mode whenever an ADC is not used. The following table shows performance parameters for the ADC. All values are preliminary. This table summarizes the differences between the STM32F0 ADC and the STM32G0 ADC. These peripherals may need to be specifically configured for correct use with the ADCs. Please refer to the corresponding peripheral training modules for more information. Several application notes dedicated to analog to digital converters are available. To learn more about ADCs, you can visit a wide range of webpages discussing successive approximation analog to digital converters.


Now, in today's episode, we're talking about what do high-earning personal trainers do? I've come up with a really huge list of what high-earning personal trainers shouldn't be doing, but my list is very simple for what you should be doing if you want to be a high-earning personal trainer. Here's what it is. Number one, you really value your time. This is something most people don't do. Most coaches out there do not value their time. Number one, they don't have a schedule, so they don't know what they're doing during the day. When they sell private training, they aren't charging premium. A high-earning personal trainer charges a premium, and they really value their time. They know what they're doing every minute of the day, and that's the difference. Low-earning personal trainers, they are scouter-brained. They're going from one thing to the next. They don't value their time. They are very disorganized. How do I know that? Because that's how I used to be. I used to do that. I had to reframe my mindset. I had to reframe my actions. That allowed me to value my time more, and when you value your time more, you're going to charge a premium for what you do. That's number one. Number two is when I look at social media, a lot of coaches out there spend two, three hours a day scrolling, looking at what other people do, and they are not producing content themselves. That could be Facebook video, Instagram video, Instagram story, Instagram live. That could be email newsletters. That could be getting on more like sales calls. That could be coming up with new connections. Those are productive items. Instead, what most coaches do is they'll be scrolling through, watching what other people do, and they pretend like they're working. When you go to bed at night, you should be a look yourself in the mirror and be like, you know what? Did I go all out today? Yes or no? Did I get distracted? If you have an iPhone, you can look at stats how long are on your phone every day. Personally, and I know this, high income or high earning coaches, they're not on their phone that much. When I get to the office here, I'm never on my phone. I use my computer to work. Not on there looking at what everyone else is doing. You shouldn't be doing that either. That's wasting time. When you look at social media, you should use that as a tool for your business. You should be uploading. You should not be watching what everyone else is doing. That's very, very key. There's a huge difference. I read this article about Mark Zuckerberg, Jeff Bezos, and Bill Gates. I read this yesterday. I talked about when they are away from work, they never even use their cell phones. They're not scrolling. They're not looking what other people are doing. They don't even let their kids do that. Think about that. The most successful people on the planet, so you should probably follow their actions. Makes sense. The next, and this has to do with number one, when you value your time, it's high earning coaches. What they do is they know exactly how to frame their program. We talked about this two podcasts ago. They sell 12-month programs. They sell programs that transform kids. They're not selling these skills-based programs, or that's all it is. What I've seen, and especially coaches in our mastermind program, the ones who are, I would say, doing six figures, like 100,000 or more, these are coaches that have realized what they offer. It's not just this one hour of training. That's very insignificant. What they do is they offer way more than that. They have mentorship programs. They have workshops. They do college recruiting. They do online programs. They have a complete package in place to transform their clients. They're not just showing up at the park and doing this. They have all of these other things that make their program complete and it makes their program the best, which allows them to charge a premium for what they do. I've seen coaches over the last couple of years, they've gone from charging $30 a session once they go through our program. They'll be charging $500 a month. That's a huge increase, but they don't just do that by just changing how much it is. They recreate their program, repackage it, make it 10 times better, and when they do that, they can increase the pricing. Again, these are things that high earning coaches do. They value their time. They're not screwing around on social media. They use social media to promote what they do, period. That's it. When they look at their program, they frame it as a 12-month program and they have additional features that enhance their program, that make their program better, that are used to actually help clients get the results faster. If you have any questions about anything I'm talking about, I would love to chat with you. There's two ways to do this. Right now, you're going to see my phone number. It's going to pop up here. Don't just call my number because I don't do any calls unless they're scheduled. You can text me here and we'll schedule a call. That's the first way you can contact me. You can go here. There's my phone number. You can go there or you can comment below this video on YouTube. You can ask me whatever questions you want. I would love to engage with you there. I'm making a point this year to engage with you more on YouTube. Have you asked more questions because I want to make sure that you're not just watching these videos and nothing happens. I want to make sure that you watch these videos you implement and when you do that, you'll get results. I want you to get results from these videos that you're watching, otherwise you're wasting your time. Again, you can text me at that number there. I'd love to connect with you and show you how you can get to the next level with your business. That's it guys. I'll see you on the next one.


I've been working on these urns or large vases depending on how healthy you're feeling and I thought I'd make one more just to show you how. This is about 7-8 pounds of clay and I'm going to put it in the middle of the wheel and it's going to turn into an urn. I'm going to center it this way just by squeezing it between the heels of my hand. Now the bigger piece, you've got to bow work it a bit more. I'm going to cone it up a bit and bend it over and one more. That's getting better. I can get rid of this excess here. It just bugs me and it gives me a bigger place to keep my needle. One more pull up. That's feeling better. My regular centering. I want to center this with a narrower base, about the base of the vase.  Makes sense. I want a taller, thinner center and that's pretty good. I'm going to open this up. I was watching a while ago. I didn't do this until I made those. I was going to say I knew how but I do know how. I haven't done this until I made these vases but I'm going to open with my fist. I'm going to open it a little bit with my hand here and then I'm just going to go down. My knuckle is going to be sort of like the drill bit. I'm just going to go straight down in there and it works really nicely. You can see this goes down there and it opens it up. I am connected here with my thumb. I don't have a lot of feeling from where I am at the end of my knuckle. My fingertips are much more sensitive to depth so I'm watching it a little bit closely. There we are. I'm going to flatten that out with my fist a bit. I'm going to put my hands in. I'm going to put my regular method of pulling my right fingers to the palm of my left hand. Actually, I'm using my knuckle. I lied. I'm using this. I'm going to do one more. I just want to open up the bottom. Now I'm going to switch and my hands are going to go the other way. Now I'm pulling my fingers right across each other and I'm just pulling across. My outside hand is raising up. My inside hand is still going across the bottom. I'm going to go down there and make it tidy. I'm going to pull it up. Notice I'm not going really fast. I was going faster when I was centering, letting the wheel do most of the work. But I want a little more control now so I'm going a little more slowly. I'm going to bring that in. I'm not going to let it get very big. And pull it up again. I always make sure it's slidy and tidy. Finger pressures are directly across from each other. I'm going to hold that clay and I'm pulling it straight up. Sometimes it gets a little awkward at the top to keep pulling. If your arms aren't long enough, you can at this point just cuddle it in and pull up.  You have to give your clay somewhere to go. You can't just push it in. It has to go up as well. I'm going to go down there and get some more clay. When you first start throwing tall cylinders, when I was teaching kids or adults, just breathe. Sometimes the people start throwing a cylinder. They're breathing in and breathing in and breathing in. If you get a really tall cylinder, you don't breathe in. You could fall over and wreck your cylinder. Just breathe. There you go. We're going to pull up again. I'm going to bring that in.  I'm going to go in there and tidy it up first. I'm going to keep that in. You want to keep the top in. You don't want it to get away from you. It's really hard to bring it in again once it goes out. If it's okay, if it's fairly thick, it's going to get thinner as you keep pulling. I'm going to start giving this guy some shape. Now my fingerprints or fingertips are right across from each other.  I'm going to keep that guy in and not worry about the thickness right now. You have to be going to have to get your arm in there. Pull it out a little bit more. That's better.  Cuddle it in. At this point, if your pot has a little bit of rhythm, don't worry about it. Because some of my favorite people have a little bit or a lot of rhythm. So don't worry about it. Pots are like people. There's very few perfect people. And there's very few perfect pots. I'm going to do what I call my six point cuddling. Because it's two, four, six. And it just sounds so cute. I don't get that much. Anyway, this is where the top quite often finds rhythm at this part of the process. And I don't care. I'm just going to now cut that out. Get rid of it. I'm going to look at my shape. It's kind of like the rest of them, I think. Now I'm supporting that. And I'm right underneath. You can maybe see where my hands are dirty. I was right underneath that shoulder and supporting right underneath and on top. So I'm holding it from both sides. Giving it some definition. And pulling up that top. I'm going to have a look at my shape. Now you don't want this part to get too tall. Because I'm going to throw a bowl upside down for a lid in a minute. And then this part is really tall. It's hard to get your bowl to fit. But I'm not going to worry too much about sponging it and making it tidy. Because I'm going to mess with it as I make the bowl fit on top. I also notice that it's slightly tapered. So the bowl will fit over top of it. Shape this way. You're going to have a problem getting your lid on there. And the inside is tidy. I'm going to get rid of that outside. A little definition right there. Tidy my taper. And cut it level. And I'll sponge it off just because I have to. It's just who I am. It's pretty much done. I do have quite a bit of clay right here. I'm going to get rid of that clay right there. I'm going to undercut it. If you have a problem with it peeling, you can, as I said before. Just put a little bit of water in there and chase that around. But this guy's going to peel. This guy, well, now it's water made a mess. This guy's going to peel fine. Very appealing, this little pot. And I've got a good place to keep my needle. I'm going to throw my wire on the floor. Pick it up. Tidy it off.  And I'll make a lid for it and talk about trimming in a bit.


In this last video for section 10.3 we are going to add one more arcs and chords theorem. So you should have a little bit of space before question number three on your note sheet. It should say arcs and chords theorem number three. I need you to go ahead and write this down. Two chords are congruent if and only if they are equidistant from the center. Okay so that means if two chords are the same distance from the center then those chords are congruent. I might have you look down at this picture real quick and you have this picture under number three on your note sheet. What this theorem says is that for example in this picture EF would have to be congruent to GH as long as the distance from the chord to the center so PQ and PR are congruent. So if this is the same distance as this then these chords have to be congruent. Okay so that's arcs and chords theorem number three. We're going to now use that to help us answer the question in number three. So first statement it does say the chords are equidistant from the center. The very first thing that I would do on my picture is mark that those are congruent. And then in the back of my mind I want to make sure that I understand because of that EF has to be congruent to GH so you might make a note of that. Alright it tells us that the radius of this circle is 15. Now when you look at this picture right now there is nothing drawn on here to show the radius. PQ and PR those are not the radii I guess I would say. If you wanted to draw in the radius you could do that in several places. You could draw PF that's the radius, you could draw PH that's the radius, you could draw PE or PG or you could go straight out here and make a new point. But I want you to understand that right now there was not a radius drawn on my picture so I had to draw it in. The other thing they tell us is that EF is 24. Well remember that the theorem we talked about, I think it's theorem number two says that if the chord is perpendicular to the diameter, which that's what we have right here, we do have a perpendicular angle here, then EQ and EF have to be congruent. Well if that's the case and if EF is 24, well then I know that QF is 12, I also know that EQ is 12 and because EF and GH were congruent that means that GR and HR are also 12. Well that answers one of our questions. One of the things we wanted to find was RH so we just figured that out, RH is 12. Alright the other thing that we want to do here is find PR. Okay so PR is this segment right here. I'm going to go ahead and label that with an A and the reason I'm going to label that with an A is that this is a right triangle where I know the leg is 12 and I know PH is the radius which they told us was 15. I can now use Pythagorean Theorem, I'm going to move my page up here a little bit and solve for PR so A squared plus 12 squared equals 15 squared. Go ahead and solve this for A, A squared plus 144 equals to 25 so A squared equals, what is that, 81 and if we solve we find out that A is 9 and A is representing PR so PR is 9. So a lot going on in this picture, you have to use a couple of the different theorems we talked about so EF is congruent to GH only because they are equidistant from the center also EF and GH or because EF and GH are congruent and because we have 90 degree angles here and here when they tell us that EF is 24 we can cut that in half to get the two sides here that are 12 that means that GR and HR also have to be 12 and then from there we have everything we need to figure out PR. Okay so for this last example we have a blank circle. What we're going to do is we're going to use all the information they give us and we're going to draw our own picture. So we're going to start with chords MO and PR and it says that those are both seven units away from the center so I'm going to put where I think the center should go and just estimating here and we know that this is an S and the reason that we know that this is S is if I continue reading the question it says the radius of circle S so if this is circle S then the center has to be S. Alright so MO and PR are both seven units away from the center so what I'm going to do is I'm going to go like this I'm going to say that that's seven and that's chord MO. I'm going to do the same thing this way. I'm going to say that this is also seven and this is chord PR. So we know that these are equidistant which now remember means that MO has to be congruent to PR because if the chords are equidistant from the center then they are congruent. Alright the circle has a radius of 15 it tells us that so I'm going to go ahead and draw in a radius. Now remember I could do that from S to O or from S to M or to SP or SR those are all radius of the circle. I mean I could even go straight out here and put a new point but if you'll notice what we're trying to eventually find is MO and PQ. Well right now I see MO is this but I don't see a Q anywhere in my picture. Well because this is PR and we're trying to find PQ chances are pretty good this is what they meant for us to put as point Q and because we're trying to find PQ and we know that this is a 90 degree angle when I draw my radius I'm going to put it here and label that as 15 because now I know this is seven this is 15 this is a right triangle so to find PQ I'll just label that A I can use Pythagorean theorem. A squared plus seven squared equals 15 squared. Let's go ahead and simplify this or solve I should say before we simplify. A squared plus 49 equals 225 subtract the 49 we get A squared equals 176 and 176 is not a perfect square so we're going to have to go ahead and simplify root 176. We can simplify into root 16 times root 11 which is 4 root 11 so that means we have found PQ which is one of the things we wanted and that's 4 root 11. Okay so the other thing we wanted to find was MO. Let's think back to the theorems we've talked about. If PQ is 4 root 11 that means that QR is also 4 root 11 and remember that PR is congruent to MO. So what we can do is we can say that PR equals 4 root 11 plus 4 root 11 or you can do 4 root 11 times 2 either way we get 8 root 11 and we know that PR back up here remember MO is congruent to PR so since we found PR is that 8 root 11 that means that MO is also 8 root 11. So what we're going to do now is we're going to


So we saw so far, so we now understand. We can multiply the original ideal impulse response by a window function Vn, that window function could be rectangular, the window function could be triangular, the window function could be cosinosoidal and could have several other shapes. Now the question is why should we have other shapes? We were beginning to answer the question in the previous lecture but now we will complete the answer. Now we saw for the case of the rectangular window and we now also make the statement that this is true for most windows that there is in the DTFT of the window, DTFT of Vn which we will call V omega typically a main lobe and several side lobes. This is typical, side lobes of decreasing amplitude. In fact just to convince ourselves, let us see how you could obtain the discrete time Fourier transform of the triangular window. Now the triangular window can be obtained by convolving the rectangular window with itself. So if you have a rectangular window between minus capital N by 2 and plus capital N by 2, let us call this Vrn for rectangular and if we convolve Vrn with itself, we get Vtn or the triangular window which looks like this minus capital N to plus capital N. It goes maybe to the highest value in a triangular fashion at 0 and then drops on either side as you go to N. Needless to say here we assume that capital N is even to make matters simple. Now that is not necessary. I mean you could always conceive of a triangular window even if N is odd but here we will make matters simple to understand how the discrete time Fourier transform looks. Now when you convolve two sequences, the discrete time Fourier transforms are multiplied. So we know what the discrete time Fourier transform of Vrn is. We have calculated it the last time. It is dt of t is sin N by 2 plus 1 omega by 2. In fact 2 N by 2 plus 1 omega by 2 divided by sin omega by 2. We have seen that the last time. All that we need to do is last time we had calculated for a length of capital N and now N has been replaced by N by 2. Now you see the triangular window is therefore going to have the dt of t squared. Let us call this Vr capital Vr omega. So obviously Vtn is going to have the dt of t Vr omega squared and we can sketch that. So Vr omega had an appearance like this. We saw it the last time. Where upon Vt omega is going to have an appearance something like this. Now the beauty is Vt omega is going to be always non-negative because where if you treat the amplitude of this is 1.  So you see this is going to be h1 squared here and this is going to be small h1 squared and therefore one thing that you see is that the drop of height from the main lobe to the first or the principle side lobe is going to get squared when you go from the rectangular to triangular window. So for example I mean just to take an example suppose you happen to find that the height of the side lobe is some percentage of the main lobe height then treating that percentage of the fraction. So if that percentage is 20 percent I mean that is too small but anyway suppose that percentage is let us say 30 percent then you treat it as 0.3. So now you are going to have 0.3 the whole squared that is going to be lower that means the side lobes are going to be of squared lower height that means the side lobes in some sense have got suppressed but again not without a cost. You see we also see where the main lobe ends. This main lobe ends at the point 2 pi by capital N is not it? 2 pi by the this width is inversely proportional to the length of the window. So you know when now what is going to happen is that when the rectangular window had a length of capital N and when it has a length of capital N by 2 now this width is going to be more and of course this width and this width are equal because it is just the square. So therefore now the width has got doubled although the side lobes have been suppressed the width has got doubled for the same length. So when you open the rectangle with the triangular window of the same length the side lobe the first the principle side lobe and therefore all the other side lobes are suppressed to the square of the original rectangular window but the width has got doubled. So there is a compromise as you see between the width of the main lobe and the strength of the side lobes. So we note this. For the same length N going from the rectangular window to the triangular window means compromise between main lobe width and side lobe strength you can understand strength in different ways. We will see which specific way we should use later but one way to understand strength is the relative height of the side lobe as compared to the main lobe. Now you see why are we interested in this compromise? We now need to go back to what we were doing the last time. We need to see what exactly these main lobes and side lobes do in degrading the frequency response. And we now go back to the drawing that we had created the last time. We had tried to analyze the effects. So we said now by the way I would like to mention a very interesting innovation which one of the students in the class suggested Vivek Kumar. So you see last time we had written we had of course observed that we need to convolve. We need to make a periodic convolution. So we had this ideal impulse response here omega c and minus omega c and we needed to convolve it with so this is the ideal I mean sorry not the ideal frequency response of the low pass filter. We were trying to observe what happens in the case of the low pass filter and we also had and you know I need to move it so I am going to draw this on a separate sheet of paper. You also had this window spectrum v omega and now we have agreed we have seen two examples and for the moment we will say this is always true that you know you have main lobe and side lobes the window spectrum. Now we said that we have essentially to move one against the other and we can choose either to move the window spectrum over the ideal response or the ideal response over the window spectrum. Now you see how do you carry out the periodic convolution? One way to carry out a periodic convolution is to truncate the two periodic functions which you are trying to convolve periodically. Now that amounts to truncating one of them to one period. So you could either choose to truncate the ideal filter response to one period and retain the periodicity of the window spectrum or you could choose to truncate the window spectrum to one period and retain the periodicity of the ideal filter. So essentially a periodic convolution means to retain the periodicity of one of those periodic functions and to restrict the other only to one period and then convolve. Now that was an interesting observation by one of the students and we will do that now. So last time we are of course started justifying that we do not but here all that we need to do is to so you know let us essentially restrict the window spectrum to one period and we will keep the you know periodicity of the ideal filter. You could do it the other way also. So now let us see once again what happens when you convolve. So I will start moving this as we did the last time. So there we are. We saw that there are three regions that we need to deal with. One region is when the main now here we are moving the window spectrum and we have agreed that this variable should be called lambda here and this variable is also lambda and this is at the point lambda equal to omega here. So when omega is far enough so that it is essentially some of the weak side loops that fall into the pass band then what do we observe as omega goes from that point and allows these side loops to move into the pass band then the resulting frequency response is the integral of the part of this window response that falls within the pass band as you vary omega. So each omega you need to calculate an integral and integral of that part of the side loop which falls into the pass band. And as you can see this area is going to oscillate weakly because there is going to be sometimes a negative contribution and then sometimes a positive contribution and sometimes a negative contribution. So there is going to be you know a smooth movement from negative to positive to negative and what is there is that as you come as omega comes closer to the pass band edge here as omega comes closer to the pass band edge the stronger side loops come into the pass band and therefore that oscillation grows and grows to a point where the principle side loop has entered the pass band as is here. Afterwards there is only going to be a growth upwards because it is the main loop which is going to enter the pass band. The main loop contributes a huge area in comparison with all the other side loops. So once the main loop begins to enter this and there is a steady upward growth of the area of the frequency response. And this growth continues all the way up to where the main loop is within is entering the pass band. So right from here where you know main loop has just begun to enter up to the point where the main loop has completely entered you have a steady growth of area. So the frequency response rises at that point. After it has thus risen to a sufficiently high level then we have again just the side loops playing their game. So the principle side loop of course first plays its game and then the weaker side loops start entering and while the principle side loop enters some of the weaker side loops are leaving from the pass band and so on and so forth. So what can we see as an overall consequence of this movement of the window function over the ideal pass band? We see the following nature of the degraded frequency response. Far away around pi you would have some weak oscillations. Then you would have a strong movement upwards and then again a strong oscillation and weaker oscillations as you go to the center and then a strong oscillation and then a downward movement and then weaker oscillations again. So this is the part where the main loop is entering the pass band. This is the part where the main loop is in the pass band and these are the parts part A and A dash where the main loop is out of the pass band. Is that clear to everybody? What is more is that these oscillations are going to be stronger just as the main loop has entered and just as the main loop is leaving because the strongest side loops are either entering or leaving there and they become weaker towards the center. The strongest oscillations are just around this point of entry and the weaker oscillations are away. Is that clear to everybody? Yes, everybody understands this and now we can also see what results in each of these quantities. So how long would this region last? How long would this region last? This region would last as long as the main loop needs to enter and that means the width of the main loop plays a role in this region. How high would these oscillations be? These oscillations would be as high as the area under the principal side loops. So the oscillatory part, the oscillatory part what we can see very clearly is the oscillatory part or the ripples in the resultant frequency response are governed by the side loop area and the transition band. Now we will give up that name, the transition band is governed by the main loop width. Please note, the transition band is the part where you move from what is effectively the stop band here to the pass band here, the effective pass band and the movement from stop band to pass band is governed by the main loop width. The oscillations in the pass band or in the stop band are governed by the side loop area. The main loop width and side loop area is what plays a role in the quality of the response. Now we know why we have to choose between windows. We had the rectangular window, we could choose the triangular window, we could choose a cosine window, we could choose several other shapes and the whole game is a compromise between main loop width and side loop area. In fact we have seen that right in the case of the rectangular and triangular window. We can at least see the compromise of main loop width to see the change of side loop area requires a little more calculation but I in fact put it as an exercise for you. Approximate the side loop, the principle side loop area for the triangular window in comparison with the rectangular window for the same length n and show that when you move from a rectangular window to a triangular window of the same length n, you are actually making a compromise between main loop width and side loop area. The triangular window is going to have a longer width, a larger width, main loop width but the side loop area would come down and in fact different shapes would have a compromise. Now as I said it is not always a compromise in you know of inconvenience. People have designed windows strategically and window design is as much of an art as a science because what you would like to do ultimately is to gain both in terms of main loop width and side loop area. Can you have less main loop width and less side loop area? Well you cannot do too much in that direction but you can do a little bit and we shall see in the next lecture one systematic approach to designing windows which in some sense offer a good compromise between main loop width and side loop area. Thank you.


Hi everyone thank you so much for joining us on today's community conversation the national popular vote. We're excited to have you here Sierra Club main has been hosting community conversations. Since the beginning of the pandemic really and it's been a wonderful way for people to come together virtually, and have some conversation on a variety of topics. And today we're super excited to be hosting the national popular vote with Margo Donis. And I would like to introduce you all to john Brodigam, who is a member of our executive committee here at Sierra Club main and he'll be helping to facilitate today's call so john I will pass it over to you. Thank you Marina it's really good to see good turnout today for this community conversation I think this is my second or third one I've done since the start of the pandemic. And it's been really valuable opportunity to connect with people I hope you'll find it as worthwhile as I have a couple housekeeping notes we asked that you keep your microphone on mute throughout the presentation to help with background noise you'll see a microphone symbol and the lower left of the screen. The microphone symbols cross to then you're muted. And next to that you'll see a video camera signal symbol.  Let you know this is being recorded if you wish to not be seen. I feel free to turn your video off and then finally, we invite you to put any questions in the chat and I'll be monitoring the chat along with Marina, and we'll have some time for q amp a. presentation and also hopefully at the end. Okay. We also at Sierra Club we acknowledge the indigenous land and sovereignty of our, the place where we are now we are in the homeland of Wabanaki the people of the dawn. We extend our respect and gratitude to the many indigenous people and their ancestors who's rich histories and vibrant communities include the Wabanaki, the malice, the mick mack, the possum aquatic and Penobscot nations and all of the native communities who have lived here for thousands of generations and what is known today as main New England and the Canadian Maritimes. This acknowledgement does not rectify the ongoing violence of settler columns of colonialism but it's rather meant to cultivate unsettling awareness of its persistence towards rebuilding reconciliation. And it's honored to collaborate with the Wabanaki as they share their stories and thanks the Abbey Museum for their leadership and decolonization efforts in Maine, and the work to create effective land acknowledgments. Okay, so today, we're really lucky to have Margot Donis of South Portland Margo has recently retired from a career in it as a systems analyst and project manager she volunteers with the legal women voters, as well as with wayside food programs and partners for health. She has two daughters who reside in southern Maine. And without further ado, I will turn it over to Margot. Wait a minute. I'm trying to share my screen and I just hold a minute. I just had this set up so perfectly. Hold a minute everyone please. It can be tricky. I have issues. No worries. Let's start it up again and start the presentation. It gets here. Can everyone see my screen. I cannot see your screen. All right, let me go back to zoom and say, share screen. Oh, share. All right, here we go. Why. Okay, when I say share, I end up not being where I want to be. And all right, just hold a minute everyone. Go back and reset. For a second there. I know. Can you see it now? Yes, we can. Yep. All right. They present and I think we're there. We're there. Perfect. Looks good. Thank you very much. All right, so this is a presentation on the introduction to the national popular vote. In this presentation, I'm going to talk about our current presidential election system. And after I've reviewed that, I'm going to talk about the national popular vote interstate compact. Followed by a discussion of some of the myths around the national popular vote. And lastly, I'm going to talk about what an election with national popular vote would be like. I'm going to start by going straight to straight to the US constitution and the statement that all states have the soul power to determine how their electors shall be appointed. Our states. Our states are given. The number of electors for each of our states is determined in the constitution as a number of our senators and the number of representatives to which that state is entitled in Congress. So Maine has four. Electors that go to the. Electoral College. And Maine and all states have the right to decide how we will appoint those electors. Here, this map shows you how electors, how many electors every state in the US have. I want you to notice a little how impactful California is with 55 electors and Texas is with 38 electors. We're going to follow them through this presentation a little bit as we go along. But this is what our map looks like as far as how many electors each of our states in their own manner get to appoint to our Electoral College. The 2020 presidential election was the results are shown here. It takes 270 votes to win on the president's presidential election because there are 538 total electors. If you sat down and added up all of these, you would come up with 538 and 270 is half plus one. So we always know who's going to win because whoever goes over that to 69 whoever hits to the magic to 70 is the winner of the presidency in our country. As you can see, there are, there's a blue side of our country, which is the west coast and a red central portion of our country. Campaigning in 2020 and in most elections these days is done in what is known as battleground states. Battleground states are states where the campaign, the presidential campaign for the candidate knows that they could go either way. They could vote for, for reliably spectate. Let's back up a little bit here. Spectator states vote reliably Republican or reliably Democrat in elections. So campaigns that are not reliably one way or the other are labeled as battleground states. And this is where campaigners go when they are campaigning. You can see California, even though it has the most electoral votes was not visited at all by any campaign, any presidential campaigner in for the 2020 election, which is a little shocking when you think of how impactful they are. Texas had three visits. They're the second, they have the second most electors. There are advantages to being a battleground state. They get more in federal grant funds. They get more money in advertising. If you or I are contributing to a presidential election, very likely our money is going to these battleground states, especially the 13 closest ones. And they will be spent on their advertising and on their campaigning. Policy favors often go to battleground states. They get more disaster declarations. They have more exemptions from certain laws. And they favor in 2020 at any rate 2019, there was faster tariff relief to battleground states. So we can see that California is a spectator state in Texas, knowing that they would matter in the next election. So. If we go back here. What we can see is that. California being a spectator state in Texas almost is a spectator state. And in Texas, there were five million votes. Cast for Democrat for the Democratic candidate, 46%. In California, there were six million votes. Cast for the Republican candidates. And all of those votes were not reflected in the result of the election because of our electoral college system, because these were spectator states. There have been several elections in the. History of the U.S. where the winner of the popular vote. Lost the election. In other words, the second, the one, the candidate who got. The lesser amount of the popular vote. One was declared the winner by the electoral college. Five times. In the history of the U.S. National popular vote, but by the electoral college that overrode the will of our national voters. In fact, these are the five times when it fell that way. There were many other elections when it was very close to following this. To having the second place winner take the prize, take, take the presidency. Question that is asked by a lot of people is, could it be different? Could we be electing our senators, our representatives, our governors? We elect them with the popular vote. Why can't we do this for presidents? This is the only election in the United States where we have an electoral college and intervening system to assign or reassign our individual votes. In this country, we do decide how we elect our president. We have the ability to decide this. We have options. Our first option is to keep everything as is, to keep our state appointed electors and keep our electoral college. Option two is to change our U.S. Constitution to determine the president via the national popular vote. The U.S. Constitution is not easy. We have a system that was put in place by the Constitution for these changes. It would require a two-third majority amendment be adopted by the U.S. Congress, and then it would need to be ratified by three-quarters of the state legislators. This is not easy to do, it would be a long process. There is an option three. Option three is to keep the electoral college as is, not to change it, but instead to go to the state laws and require that their state appointed electors vote for the national popular vote winner. And that's when we at the beginning, the second slide that I showed you, showed that in the Constitution, the states have the sole power to determine how their electors will be appointed. So with national popular vote, if we can get enough states to decide to appoint their electors according to the national vote winner, then we will change how we have elected our president. That's what the national popular vote interstate compact The states in the compact commit their electoral votes to the winner of the national vote. The compact is in effect when 270 of the electoral votes are committed. 15 states today commit 195 electoral votes. We need 75 more, of which Maine will be four of those 75. There are other states today considering joining this compact. The compact is constitutional. It doesn't abolish the electoral college. We don't need a constitutional amendment to do this compact. We favor voters, not parties. It's nonpartisan. There are small states, large states, urban states in this compact. As you can see listed here are the 15 states in the district of Columbia that are in our compact. These represent these control 195 electoral votes. The national popular vote interstate compact guarantees every vote in every state in every presidential election will be equal and relevant. The candidate with the most votes will win. And we expect that candidates will be motivated to seek voter support in all 50 states. I want to move now to some common myths about the national popular vote and what it will or won't do. I'm going to address the myth about our small states that they may lose an advantage. The second myth is will the big cities dominate an election. The third is didn't the founders design the electoral college for a reason. And the fourth is do only a minority of voters support national popular vote. Let's start with a small state advantage. 12 of the small states divide evenly as far as how they reliably vote today. Six of those states reliably vote Republican and six reliably vote Democrat. So really those 12 states are spectator states. They're not getting visits. They're not getting any favors. No campaign visits went to Maine's first district. And two campaign visits went to Maine's second district. And two campaign visits went to Maine's first district.  Four campaign visits to the battleground state of New Hampshire because it was a battleground state. Small states are supporting the national popular vote. Vermont, Hawaii, Delaware, Rhode Island, District of Columbia. And so for one thing, from this 2010 census, the population of the big cities is about even with the population of rural America. So it's expected that if our national popular vote compact goes into effect, it will matter to campaigns that they visit where the population lives and we're evenly divided. Why isn't that the next question is on what did the framers want in the original Constitution? There were a lot of things the framers outlined that are no longer there today. They expected the lecture in the original arrangement in the original 13 states, but they often, more often selected their state legislatures or had their state legislatures appoint their electors to the electoral college, not the state citizens. State citizens today are the voting for president and that's how things have changed over the years. In the original Constitution, enslaved people, women, men without property were excluded. That's been changed with amendments over the years. In the original electoral college, the first place winner became president, the second place winner became vice president, and this was a terrible problem in the election of 1800 when Jefferson against Burr tied. So that was changed quite quickly after that election. And the original Constitution framers wanted to make a process for amendments. They wanted the Constitution to be able to be amended not too easily, but they also wanted a process which I outlined earlier where you would adopt an amendment and then ratify the amendment. The other myth is that a lot of Americans do not support national popular vote. This is simply not true. In 1960, Senator Margaret Chase Smith from Maine cosponsored a national popular vote bill. In 1970, we came very close to passing amending the Constitution to have a national popular vote for president. At that time, 80% of U.S. voters supported a national popular vote for president. And the U.S. House passed an amendment for this. The U.S. Senate filibustered it and it died being defeated by five votes. We really came close in 1970. A 2019 polls show 61% of Mainers support national popular vote. And as state demographics are changing to be more competitive, national popular vote is preferred by many party leaders. Lastly, let me turn to what an election with national popular vote would be like. The winner would be seen as more legitimate. Campaign platforms would address more national issues instead of favoring battleground state issues. One example of this is is that campaigns often talk about manufacturing and about coal production and so on. Where those are interests of many of the battleground states. Campaigns sell them talk about logging, for example, which is a main interest in the North West. They sell them talk about things going on in California with the IT industry or with wildfires and water problems. It's expected that national issues will change. And campaigns and what they stand for will follow the national issues that we have. Vice presidents can be chosen from any state versus a battleground state. Today, when campaigns are run, the vice president is carefully chosen so that he or she comes from a battleground state. And it's expected there will be more voter participation in 2020. 60% of voters turned out in battleground states. 60% of voters turned out in spectator states. Campaign visits would be made to most states. Campaign visits would be made equally to cities and rural areas. Spectator state campaigns will get more support from their national party and down ballot candidates in spectator states will benefit from presidential candidate events. Lastly, nationwide, Americans will vote as Americans, not as red state Americans or blue state Americans. And my question here is, I'm thinking we would share more of our political views with our neighbors, our families and our friends who may not agree with us. I don't think there will be more votes with our neighbors. I'm probably talking about more political issues with them, which today I kind of avoid. What's the point? Because I don't think their vote is going to count because they're voting. I know that my district will go in a certain direction. That's how we live today. I think we would be less polarized if we all knew that all of our votes counted equally. That to me is a big benefit. If you want to take action around national popular vote, I can share this. With you, nationalpopularvote.com for more information. Here's their link. Let the people pick the president is an important book for book discussions. You can subscribe to our e-mail list. And you can like our mainers for national popular vote on Facebook. And lastly, we have a link with the national popular vote. We have a link with the representative with an e-mail or with a phone call around national popular vote. We have tools for writing a letter to the editor and we invite your local library to co-host a book group with the league and to attend our monthly training for national popular vote. Thank you. I appreciate that. Why don't we take some questions? I do see one question, which was from me. And I'll pass this along. Can you give an update on the status of the legislation and the main legislature for the coming session? I don't know. I don't know. I don't know if it stayed in the committee. It did not get voted out to proceed to the floor. So we don't expect in this coming year, 2022 that it will be reintroduced. However, in 2023, we expect that it will be reintroduced. And our efforts right now are trying to. To continue to fill their questions and so on. Another piece that I didn't, I can elaborate on a little bit. If Maine were to join the interstate compact. We would, let's say we joined. In 2023. Doesn't become active until enough states join to reach the 270 threshold. So let's say that threshold is met. We get like Virginia and North Carolina in, and we end up with the 270. And now January of 2024 comes up. All of the candidates will know that they have to vote, have to campaign nationally because this is an effect. And. Any state that wanted to pull out of the compact. Cannot do it in the last six months before the election. So from July one until January 20th, they're required to stay in the compact. They cannot withdraw. So that the compact is not in effect. And I'm sure if that makes sense. But that's part of how the compact reads. So even if we join this year. It just doesn't come into effect until enough have joined. I'll ask another question just to keep the conversation going. Is there any. Opposition to this idea in, in Maine. And if so, What kind of arguments are they making. In 2019, we came really close to passing this bill. In 2019. Again, I don't believe any Republicans voted for it. But in 2019, the house, the state house passed it, the state Senate passed it, went back to the house. And after a couple of different votes. It was switched and not passed by like one vote. We came very close in 2019. Again, the small state argument saying means a small state. We get more because we have these four electors. Somehow we get an advantage. Again, we're not really getting an advantage as I showed. Arguments against it are given by. Many conservative. People thinking that. They won't benefit from it and that. The elections that have gone their way in since 2020 have been two different elections. But there are many conservative leaders, Michael steel among them, who are on the national popular vote board. And who want. Republicans to campaign all across the country. So, there are states that are almost going to turn blue. Texas being one of them. And that would flip the electoral college in the Democrats. Benefit. So it's really dicey whether conservatives can say, well, we benefit, so we really don't want to change it. So, I think that's a good point. I think that's a good point too. Probably within a few years from now. And a lot of conservatives are seeing this as. Very possible. Can you remind us other than Maine, what other states are likely where this is. Could be come up for a decision in the next few years. That's something I don't have as a list. I can get that for you and send it to you later. So, there are multiple states being looked at it. So. I can get you a list. Yeah. Are there any other questions from the folks who are here today? There's a question is the League of Women Voters pushing this in any particular state. And I assume that we don't really have an answer to that right now, but we can get back to you on that. On that issue. Is there anything that people can do to get involved in this? If we want to get involved here in Maine. Again, I'll share the last two slides. After this, and you can put it, send it out to the people on the call on. You can come to a monthly meeting when we do a training. You can, we have ways of showing you how to write letters to the editor or contact your representative. You can become a speaker volunteer be a speaker like me. Yeah. And we did a lot of work in sadly last year. They didn't, didn't pan out, but we, when it was in committee and we wanted it to be voted out. So, so to the floor are our group did quite a bit of. Reaching out to voters from different districts in Maine, different municipalities, so they could call their state rep and encourage them to support. So. We expect to be doing that kind of work too in 2023 when this comes back up again and is in committee again. I mean, we attended it by zoom, different committee hearings on this and we're able to speak. So it was educational about how to do. I'm political meetings via zoom. We felt like a lot of the representatives. We're under informed about national popular vote. Interstate compact was, I think people think it's a little more complicated than it is. And we felt like education was, was required or reaching out to them was helpful. So. Do you think that the national popular vote, if it was approved. Would, would change anything with respect to the kinds of policies that are most important to us. Not just our core policies regarding energy, the environment, health. And preservation conservation, but also our policies of equity and inclusion. Would those get more attention under a national popular vote system. I think. One of the things that is happening is that so much money is given to candidates who only spend it in. In a handful of battleground states. So if you took all of that money and you try to get all Americans to vote. Then you would also care about Americans who may be in a minority. But I think it's important to think about that. For example, I remember hearing after the election in Texas that. There were local. Activists who wanted to reach out to local radio stations that a lot of Texans listen to, but they didn't have any money to reach out to those hosts and find ways to speak. So I think it's important to think about that. I think it's important to think about that. I think it's important to think about those activists and they, they were denied money from the national. Election group. So we would care, I think about. All Americans. And especially some of these minority groups that. That matter a lot to us. I'm not sure if that's answering your question, but. I think that the group that's working on that. The group that's working on it. And I think that the issues on all districts. And all regions of the country would start to happen. Well, as, as everybody knows, the Sierra club has a. Very strong. Democracy agenda. In all matters. And supports a wide variety of measures to make sure that the voice of the people. money or flukes in our election systems or anything like that. So I think, you know, I think that this fits right in the fact agenda, even though I don't believe the CR club nationally has taken a position on this as of yet, unless I'm mistaken. Yeah, we're the only democracy in the world that has anything like this electoral college. The lion's share of democracies do a direct election for president. Another person has commented that there we see how many people support things like anti choice and anti women's health measures in Texas and don't members of Congress who don't take any action on climate change, even though these are positions that are very popular with the public. They're just really the electoral system doesn't seem to be responding to that. All right, I mean if a campaign if if they started campaigning in somewhere like California I imagine they'd start getting questions about how can you help us with this the wildfire wildfire problem and things of that nature. They're not being asked those questions now and in Michigan and Ohio, where they go. You know, the campaigns are simply going to care more about all issues. That's the expectation. Right. Are there any other questions for Marco. Well, maybe we can wrap it at that point then and thank you for everybody for joining and participating and great job Marco for your presentation really salute you for your work in this area and appreciate your bringing us up to date and giving us a thorough background or on on NPV in Maine and in the country. So we really appreciate it and I'll turn it back to Marina. Yes, thank you john and I'm going to share my screen just for a couple of wrap up slides. Just wanted to thank you so much Marco for joining us today and for the great conversation and sharing your expertise on such an important topic with us it was really a pleasure to have you so thank you. And thank you for everyone who joined us today. Marco is going to be sending those couple of slides to me so I'll be sure to email everyone with those slides and some take action items for you. I also like to invite everyone to stay updated on our work by following Sierra Club main on social media. You can also follow us on our website or work on our website and you can subscribe to our newsletter at Sierra Club. org slash main. And before we take off, if my time changes here. I just wanted to invite everyone to our next community conversation, which is next week next Tuesday, October 12 at noon. I'm Marina Fyalkoff of the wild seed project will walk us through what it means to rewild in 10 action steps. So rewilding really helps to safeguard wildlife habitat, support the biodiversity and mitigate the effects of climate change. So if you are interested in that I will actually put a link to register in the chat. We hope to see you there. Other than that, thank you everyone and thank you margo and john for your help facilitating it's been a pleasure. And thank you for having me inviting us to talk. Thank you.