Lp norms
The norm of an dimensional vector (signal) is defined as
(5.27) 
Special Cases

norm
(5.28)
 Sum of the absolute values of the elements
 ``City block'' distance

norm
(5.29)
 ``Euclidean'' distance
 Minimized by ``Least Squares'' techniques

norm
In the limit as , the norm of is dominated by the maximum element of . Optimal Chebyshev filters minimize this norm of the frequencyresponse error.
Filter Design using Lp Norms
Formulated as an norm minimization, the FIR filter design problem can be stated as follows:
(5.31) 
where
 FIR filter coefficients
 suitable discrete set of frequencies
 desired (complex) frequency response
 obtained frequency response (typically fft(h))
 (optional) error weighting function
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Optimal Chebyshev FIR Filters
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Conclusions