cupyx.scipy.signal.freqz#

cupyx.scipy.signal.freqz(b, a=1, worN=512, whole=False, plot=None, fs=6.283185307179586, include_nyquist=False)[source]#

Compute the frequency response of a digital filter.

Given the M-order numerator b and N-order denominator a of a digital filter, compute its frequency response:

            jw                 -jw              -jwM
   jw    B(e  )    b[0] + b[1]e    + ... + b[M]e
H(e  ) = ------ = -----------------------------------
            jw                 -jw              -jwN
         A(e  )    a[0] + a[1]e    + ... + a[N]e
Parameters:

  • b (array_like) – Numerator of a linear filter. If b has dimension greater than 1, it is assumed that the coefficients are stored in the first dimension, and b.shape[1:], a.shape[1:], and the shape of the frequencies array must be compatible for broadcasting.

  • a (array_like) – Denominator of a linear filter. If b has dimension greater than 1, it is assumed that the coefficients are stored in the first dimension, and b.shape[1:], a.shape[1:], and the shape of the frequencies array must be compatible for broadcasting.

  • worN ({None, int, array_like}, optional) –

    If a single integer, then compute at that many frequencies (default is N=512). This is a convenient alternative to:

    cupy.linspace(0, fs if whole else fs/2, N,
              endpoint=include_nyquist)

    Using a number that is fast for FFT computations can result in faster computations (see Notes).

    If an array_like, compute the response at the frequencies given. These are in the same units as fs.

  • whole (bool, optional) – Normally, frequencies are computed from 0 to the Nyquist frequency, fs/2 (upper-half of unit-circle). If whole is True, compute frequencies from 0 to fs. Ignored if worN is array_like.

  • plot (callable) – A callable that takes two arguments. If given, the return parameters w and h are passed to plot. Useful for plotting the frequency response inside freqz.

  • fs (float, optional) – The sampling frequency of the digital system. Defaults to 2*pi radians/sample (so w is from 0 to pi).

  • include_nyquist (bool, optional) – If whole is False and worN is an integer, setting include_nyquist to True will include the last frequency (Nyquist frequency) and is otherwise ignored.

Returns:

  • w (ndarray) – The frequencies at which h was computed, in the same units as fs. By default, w is normalized to the range [0, pi) (radians/sample).

  • h (ndarray) – The frequency response, as complex numbers.

See also

freqz_zpk, sosfreqz, scipy.signal.freqz

Notes

Using Matplotlib’s matplotlib.pyplot.plot() function as the callable for plot produces unexpected results, as this plots the real part of the complex transfer function, not the magnitude. Try lambda w, h: plot(w, cupy.abs(h)).

A direct computation via (R)FFT is used to compute the frequency response when the following conditions are met:

  1. An integer value is given for worN.

  2. worN is fast to compute via FFT (i.e., next_fast_len(worN) <scipy.fft.next_fast_len> equals worN).

  3. The denominator coefficients are a single value (a.shape[0] == 1).

  4. worN is at least as long as the numerator coefficients (worN >= b.shape[0]).

  5. If b.ndim > 1, then b.shape[-1] == 1.

For long FIR filters, the FFT approach can have lower error and be much faster than the equivalent direct polynomial calculation.