scipy.signal.firwin2(numtaps, freq, gain, nfreqs=None, window='hamming', nyq=None, antisymmetric=False, fs=None)[source]

FIR filter design using the window method.

From the given frequencies freq and corresponding gains gain, this function constructs an FIR filter with linear phase and (approximately) the given frequency response.


numtaps : int

The number of taps in the FIR filter. numtaps must be less than nfreqs.

freq : array_like, 1D

The frequency sampling points. Typically 0.0 to 1.0 with 1.0 being Nyquist. The Nyquist frequency is half fs. The values in freq must be nondecreasing. A value can be repeated once to implement a discontinuity. The first value in freq must be 0, and the last value must be fs/2.

gain : array_like

The filter gains at the frequency sampling points. Certain constraints to gain values, depending on the filter type, are applied, see Notes for details.

nfreqs : int, optional

The size of the interpolation mesh used to construct the filter. For most efficient behavior, this should be a power of 2 plus 1 (e.g, 129, 257, etc). The default is one more than the smallest power of 2 that is not less than numtaps. nfreqs must be greater than numtaps.

window : string or (string, float) or float, or None, optional

Window function to use. Default is “hamming”. See scipy.signal.get_window for the complete list of possible values. If None, no window function is applied.

nyq : float, optional

Deprecated. Use `fs` instead. This is the Nyquist frequency. Each frequency in freq must be between 0 and nyq. Default is 1.

antisymmetric : bool, optional

Whether resulting impulse response is symmetric/antisymmetric. See Notes for more details.

fs : float, optional

The sampling frequency of the signal. Each frequency in cutoff must be between 0 and fs/2. Default is 2.


taps : ndarray

The filter coefficients of the FIR filter, as a 1-D array of length numtaps.


From the given set of frequencies and gains, the desired response is constructed in the frequency domain. The inverse FFT is applied to the desired response to create the associated convolution kernel, and the first numtaps coefficients of this kernel, scaled by window, are returned.

The FIR filter will have linear phase. The type of filter is determined by the value of ‘numtaps` and antisymmetric flag. There are four possible combinations:

  • odd numtaps, antisymmetric is False, type I filter is produced
  • even numtaps, antisymmetric is False, type II filter is produced
  • odd numtaps, antisymmetric is True, type III filter is produced
  • even numtaps, antisymmetric is True, type IV filter is produced

Magnitude response of all but type I filters are subjects to following constraints:

  • type II – zero at the Nyquist frequency
  • type III – zero at zero and Nyquist frequencies
  • type IV – zero at zero frequency

New in version 0.9.0.


[R245]Oppenheim, A. V. and Schafer, R. W., “Discrete-Time Signal Processing”, Prentice-Hall, Englewood Cliffs, New Jersey (1989). (See, for example, Section 7.4.)
[R246]Smith, Steven W., “The Scientist and Engineer’s Guide to Digital Signal Processing”, Ch. 17.


A lowpass FIR filter with a response that is 1 on [0.0, 0.5], and that decreases linearly on [0.5, 1.0] from 1 to 0:

>>> from scipy import signal
>>> taps = signal.firwin2(150, [0.0, 0.5, 1.0], [1.0, 1.0, 0.0])
>>> print(taps[72:78])
[-0.02286961 -0.06362756  0.57310236  0.57310236 -0.06362756 -0.02286961]

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