`scipy.signal._fir_filter_design:firwin2`

source: /scipy/signal/_fir_filter_design.py :577

Signature

   def     firwin2 (    numtaps    ,    freq    ,    gain    ,  * ,     nfreqs    =  None   ,    window    =  hamming   ,    antisymmetric    =  False   ,    fs    =  None     )

Summary

FIR filter design using the window method.

Extended Summary

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

Parameters

numtaps : int: The number of taps in the FIR filter. numtaps must be less than 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 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. 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 numtaps. nfreqs must be greater than numtaps.
window : string or (string, float) or float, or None, optional: Desired window to use. Default is 'hamming'. The window will be symmetric, unless a suffix '_periodic' is appended to the window name (e.g., 'hamming_perodic') Consult get_window for a list of windows and required parameters. If None, no window function is applied.
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.

Returns

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

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 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

Array API Standard Support

firwin2 has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ✅                   
PyTorch               ✅                     ⛔                   
JAX                   ⚠️ no JIT             ⛔                   
Dask                  ⚠️ computes graph     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

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])

✓

Aliases

scipy.signal.firwin2