BUILT-IN MATHEMATICA SYMBOL

# EquirippleFilterKernel

EquirippleFilterKernel[{{{L1, R1}, {L2, R2}, ...}, {a1, a2, ...}}, n]
creates a finite impulse response (FIR) filter kernel of length n with an equiripple amplitude response, given the specified left and right band edge frequencies and amplitudes .

EquirippleFilterKernel[{{{L1, R1}, {L2, R2}, ...}, {a1, a2, ...}, {w1, ...}}, n]
uses relative weights for each frequency band.

EquirippleFilterKernel[{"type", {{{L1, R1}, ...}, ...}, n]
creates a filter of the specified .

## Details and OptionsDetails and Options

• EquirippleFilterKernel returns a numeric list of length n of the impulse response coefficients of an FIR filter that has the minimum Chebyshev (minimax) error.
• Possible filter specification types are:
•  "Multiband" multiple passband and stopband filter specification (default) "Differentiator" differentiator filter "Hilbert" Hilbert filter
• Frequencies should be given in an ascending order such that .
• The lengths of the lists of frequency bands, amplitudes, and weights should be the same.
• Amplitude values should be non-negative. Typically, values specify a stopband, and values specify a passband.
• The kernel ker returned by EquirippleFilterKernel can be used in ListConvolve[ker, data] to apply the filter to data.
• The following options can be given:
•  "GridDensity" 8 frequency domain sampling density factor WorkingPrecision MachinePrecision precision to use in internal computations

## ExamplesExamplesopen allclose all

### Basic Examples (1)Basic Examples (1)

Length-15 equiripple lowpass kernel:

 Out[1]=

Magnitude plot of the filter:

 Out[2]=