1) Does this have something to do with aesthetics? Because engineers like the relative uniformity of an equiripple response, as opposed to the more 'organic' response of other methods.
2) Is it because an equiripple design allows the maximum error to be quoted as a design parameter?
3) Does it have something to do with robustness and L-Inf norms? Because the maximum error is minimized.
4) ... (Others?)
The price paid for these features is that the overall error, or deviation from the desired response, is greater than what is achievable by simply minimizing the (integral or sampled) error function, possibly weighted by some function.
If it is possible to reduce the error in some parts of the the spectrum, for an FIR or an IIR filter, then why not do it? Is non uniformity really that objectionable?
I would be interested to hear your thought on this.
In my opinion equi-ripple filter designs are more robust. Especially these are more robust against random errors of all sort (system errors, measurement errors).
Hi Hugh,
The 'standard' Parks-McCellan Remez Exchange algorithm (Equi-ripple) is widely applied because it is well understood and delivers in general shorter tap-length FIR filters compared to error-minimized, interpolation or windowing approaches. It has nothing to do with the transition from e.g. pass-band to stop-band. This is a matter a tap amount. Nice lecture slides are found here: http://www.vyssotski.ch/BasicsOfInstrumentation/SpikeSorting/Design_of_FIR_Filters.pdf
Furthermore, the above mentioned equi-ripple approach (besides others) is implemented in Matlab/Signal Processing Toolbox.
One advantage of equiripple (digital) filters over flat response digital filters is that approximate ideal filter response can achieve with minimum value of the order. Otherwise if we use flat response filter (chebyshev) that higher values of filter order is used which is itself includes complex computations that is not feasible. so that we can prefer equiripple filters over digital one.
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