firwin2(numtaps, freq, gain, nfreqs=None, window='hamming', nyq=None, antisymmetric=False, fs=None)

From the given frequencies :None:None:`freq` and corresponding gains :None:None:`gain`, this function constructs an FIR filter with linear phase and (approximately) the given frequency response.

Notes

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 :None:None:`numtaps` coefficients of this kernel, scaled by :None:None:`window`, are returned.

The FIR filter will have linear phase. The type of filter is determined by the value of 'numtaps` and :None:None:`antisymmetric` flag. There are four possible combinations:

• odd :None:None:`numtaps`, :None:None:`antisymmetric` is False, type I filter is produced

• even :None:None:`numtaps`, :None:None:`antisymmetric` is False, type II filter is produced

• odd :None:None:`numtaps`, :None:None:`antisymmetric` is True, type III filter is produced

• even :None:None:`numtaps`, :None:None:`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

Parameters

numtaps : int

The number of taps in the FIR filter. :None:None:`numtaps` must be less than :None:None:`nfreqs`.

freq : array_like, 1-D

The frequency sampling points. Typically 0.0 to 1.0 with 1.0 being Nyquist. The Nyquist frequency is half :None:None:`fs`. The values in :None:None:`freq` must be nondecreasing. A value can be repeated once to implement a discontinuity. The first value in :None:None:`freq` must be 0, and the last value must be fs/2 . Values 0 and fs/2 must not be repeated.

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 :None:None:`numtaps`. :None:None:`nfreqs` must be greater than :None:None:`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 :None:None:`freq` must be between 0 and :None:None:`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 :None:None:`cutoff` must be between 0 and fs/2 . Default is 2.

Returns

taps : ndarray

The filter coefficients of the FIR filter, as a 1-D array of length :None:None:`numtaps`.

FIR filter design using the window method.

See Also

firls

firwin

minimum_phase

remez

Examples

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]

See :

Back References

The following pages refer to to this document either explicitly or contain code examples using this.

scipy.signal._fir_filter_design.firwin scipy.signal._fir_filter_design.firwin2 scipy.signal._fir_filter_design.remez scipy.signal._fir_filter_design.minimum_phase scipy.signal._signaltools._freq_domain_conv scipy.signal._signaltools.fftconvolve scipy.signal._signaltools.choose_conv_method scipy.signal._fir_filter_design.firls scipy.signal._signaltools.convolve scipy.signal._signaltools.correlate2d scipy.signal._signaltools.convolve2d scipy.signal._fir_filter_design.kaiserord scipy.signal._signaltools.oaconvolve scipy.signal._signaltools.correlate

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