Signals and Systems/Filter Implementations
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Now that we know the basic types of filters (lowpass, bandstop, etc...), we can start looking at some particular implementations of filters. It is possible to design a new type of filter, "from scratch", but the filters listed here have been studied extensively, and designs for these filters (including circuit designs to implement them) are all readily available.
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[edit] Butterworth Filters
A butterworth filter is a type of filter this is both easy to implement, and also offers consistent, smooth results. Butterworth filters, however, don't have a particularly steep drop-off, and if drop-off is the biggest concern, another type of filter should be used.
[edit] Butterworth Polynomials
[edit] Chebyshev Filters
In comparison to Butterworth filters, Chebyshev filters have much steeper roll-off, but at the same time suffer from a rippleing effect in the passband that can cause unspecified results. Also, chebyshev equations utilize a complex string of trigonomic and arc-trigonometric functions, which can be difficult to deal with mathematically.
Chebyshev filters can be divided into two types: Type I and Type II Chebyshev filters.
[edit] Ripple Effect
Chebyshev filters exhibit a ripple-shape in the frequency response of the filter. The locations of the ripples varies with the type of filter (discussed below).
[edit] Chebyshev Type I
Chebyshev Type I filters have ripples in the passband.
[edit] Chebyshev Type II
Chebyshev Type II filters have ripples in the stopband.
[edit] Chebyshev Polynomials
[edit] Elliptic Filters
Elliptic filters, like Chebyshev filters, suffer from a ripple effect. However, unlike the type 1 and Type 2 Chebyshev filters, Elliptic filters have ripples in both the passband and the stopband. To counteract this limitation, Elliptic filters have a very aggressive rolloff, which often more than makes up for the ripples.
[edit] Bessel Filters
[edit] Filter Design
Using what we've learned so far about filters, this chapter will discuss filter design, and will show how to make decisions as to the type of filter (Butterworth, Chebyshev, Elliptic), and will help to show how to set parameters to acheive a set of specifications.
