Common Transfer Function Families
While any LTI system can be described by some transfer function or another, there are certain "families" of special transfer functions that are commonly used. Typical infinite impulse response filters are designed to implement one of these special transfer functions.
Some common transfer function families and their particular characteristics are:
- Butterworth filter – maximally flat in passband and stopband for the given order
- Chebyshev filter (Type I) – maximally flat in stopband, sharper cutoff than Butterworth of same order
- Chebyshev filter (Type II) – maximally flat in passband, sharper cutoff than Butterworth of same order
- Bessel filter – best pulse response for a given order because it has no group delay ripple
- Elliptic filter – sharpest cutoff (narrowest transition between pass band and stop band) for the given order
- Optimum "L" filter
- Gaussian filter – minimum group delay; gives no overshoot to a step function.
- Hourglass filter
- Raised-cosine filter
Read more about this topic: Transfer Function, Signal Processing
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