creates a finite impulse response (FIR) filter kernel using a frequency sampling method from amplitude values ai.


creates an FIR filter kernel of type m.

Details and Options

  • Possible types m for FIR filters created for a list {a1,a2,,ak} of amplitudes are:
  • The default type is .
  • The frequency sampling method uniformly samples the frequency domain from 0 to .
  • FrequencySamplingFilterKernel by default uses a sampling of the frequency domain at integer multiples of , where is the length of the filter. With "Shifted"->True, the frequencies are shifted from 0 by . »
  • Amplitude values should be non-negative. Typically, values ai=0 specify a stopband, and values ai=1 specify a passband.
  • The kernel ker returned by FrequencySamplingFilterKernel can be used in ListConvolve[ker,data] to apply the filter to data.
  • FrequencySamplingFilterKernel takes a WorkingPrecision option that specifies the precision to use in internal computations. The default setting is WorkingPrecision->MachinePrecision.


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Basic Examples  (1)

A symmetric odd-length FIR lowpass kernel:

Scope  (7)

A type 1 FIR kernel with even symmetry and odd length:

A type 2 FIR kernel with even symmetry and even length:

A type 3 FIR kernel with odd symmetry and odd length:

A type 4 FIR kernel with odd symmetry and even length:

A symmetric odd-length FIR highpass kernel:

A symmetric even-length FIR bandpass kernel:

A full-band differentiator FIR kernel:

Options  (1)

"Shifted"  (1)

By default, first frequency is sampled at 0:

With "Shifted"->True, first frequency is offset from 0 by :

Applications  (2)

Smooth data by convolving it with a lowpass filter kernel:

Apply a derivative filter to rows of an image:

Properties & Relations  (1)

Apply a window to an FIR filter to reduce ripple in its magnitude response:

Introduced in 2012