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BUILT-IN MATHEMATICA SYMBOL
LeastSquaresFilterKernel
LeastSquaresFilterKernel[{{
1, ..., k-1}, {a1, ..., ak}}, n]
creates a k-band finite impulse response (FIR) filter kernel of length n designed using a least squares method, given the specified frequencies 
and amplitudes 
.
LeastSquaresFilterKernel[{"type", spec}, n]
uses the full filter specification 
.
Details and Options
- LeastSquaresFilterKernel returns a numeric list of length n of the impulse response coefficients of an FIR filter that has the minimum mean-squared error.
- The impulse response of the filter is computed using the inverse discrete-time Fourier transform.
- In LeastSquaresFilterKernel[{"type", spec}, n], filter specification can be any of the following:
-
{"Lowpass", c}lowpass filter with cutoff frequency 
{"Highpass", c}highpass filter with cutoff frequency 
{"Bandpass",{ c1,c2}}bandpass filter with pass band from 
to 
{"Bandstop",{ c1,c2}}bandstop filter with stop band from 
to 
{"Multiband",{ 1,...,k-1},{a1,...,ak}}multiband filter specification with k bands {"Differentiator", c}differentiator filter with cutoff frequency 
{"Hilbert", c}Hilbert filter with cutoff frequency 
- If
is omitted, 
is assumed. - Frequencies should be given in an ascending order such that
. - Amplitude value
corresponds to the frequency band 
to 
, and amplitude 
corresponds to the frequency band 
to 
. - Amplitude values should be non-negative. Typically, values
specify a stopband, and values 
specify a passband. - The kernel, ker, returned by LeastSquaresFilterKernel can be used in ListConvolve[ker, data] to apply the filter to data.
- LeastSquaresFilterKernel takes a WorkingPrecision option, which specifies the precision to use in internal computations. The default setting is WorkingPrecision->MachinePrecision.
New in 9
