derived filter parts article section rely reader knowledge complex representation knowledge frequency domain representation signals derived filters type filters type electronic filter designed image method invented early 1920s filter type originally intended use telephone improvement existing constant type filter main problem addressed need achieve better match filter terminating general filters designed image method fail exact match type filter big improvement suitable choice type filter section advantage rapid transition cut frequency pass band pole inside stop band despite advantages type filters frequencies past pole response starts rise types poor stop band rejection reason filters designed type sections designed composite filters mixture type type sections different values different points performance types background patented matching network essence called type filters image method pre dated publication constant type design type filter based published image analysis theory type filters popular type filters image designed filters general rarely designed having superseded advanced network synthesis methods building block derived filters image filters network called half section composed series derived filter derivative constant filter starting point design values derived constant prototype given formula nominal filter designer arbitrary constant different kinds derived section series obtain derived series half section designer determines added image image original constant section general formula image additional required shown formula obtain derived half section added image image original half section additional required shown formula general arrangements circuits shown right specific example low pass section consequence design derived half section match type section type section value match type section value sides offer type operating frequency low pass half section shown cut frequency type type given formula pole occurs formula clear smaller values produce formula closer cut frequency formula cut despite cut brings unwanted stop band response type closer cut frequency making difficult filtered subsequent sections value chosen usually compromise conflicting requirements practical limit small inherent resistance effect causing pole deep longer genuinely infinite pole slope cut steep effect marked formula brought closer formula improvement response image following expressions image referenced low pass prototype section scaled nominal frequencies expressions scaled cut frequency series sections image series section given formula constant section formula sections image section given formula constant section formula type section image type low pass section purely real cut frequency purely imaginary chart seen closest match constant pure resistance termination occurs approximately transmission parameters derived section general transmission parameters half section given formula half sections formula particular example low pass section transmission parameters solve differently frequency bands formula transmission formula formula transmission parameters formula formula transmission parameters formula prototype plots shown image phase change plots low pass prototype filter section prototype cut frequency nominal produced filter half section henry prototype scaled frequency scaled desired values low pass prototype transformed high pass band pass band stop types application suitable frequency sections half sections form composite filter like face like combinations circuits formed identical half sections faces section called section faces section formed section additions half sections forms ladder network start end series elements born mind characteristics filter predicted image method accurate section terminated image usually true sections end usually terminated fixed resistance section end filter accurate prediction effects terminating masked intervening sections usual provide half half sections ends filter value gives best match termination
M-derived filter