cupyx.scipy.signal.invresz#
- cupyx.scipy.signal.invresz(r, p, k, tol=0.001, rtype='avg')[source]#
Compute b(z) and a(z) from partial fraction expansion.
If M is the degree of numerator b and N the degree of denominator a:
b(z) b[0] + b[1] z**(-1) + ... + b[M] z**(-M) H(z) = ------ = ------------------------------------------ a(z) a[0] + a[1] z**(-1) + ... + a[N] z**(-N)
then the partial-fraction expansion H(z) is defined as:
r[0] r[-1] = --------------- + ... + ---------------- + k[0] + k[1]z**(-1) ... (1-p[0]z**(-1)) (1-p[-1]z**(-1))
If there are any repeated roots (closer than tol), then the partial fraction expansion has terms like:
r[i] r[i+1] r[i+n-1] -------------- + ------------------ + ... + ------------------ (1-p[i]z**(-1)) (1-p[i]z**(-1))**2 (1-p[i]z**(-1))**n
This function is used for polynomials in negative powers of z, such as digital filters in DSP. For positive powers, use invres.
- Parameters:
r (array_like) – Residues corresponding to the poles. For repeated poles, the residues must be ordered to correspond to ascending by power fractions.
p (array_like) – Poles. Equal poles must be adjacent.
k (array_like) – Coefficients of the direct polynomial term.
tol (float, optional) – The tolerance for two roots to be considered equal in terms of the distance between them. Default is 1e-3. See unique_roots for further details.
rtype ({'avg', 'min', 'max'}, optional) – Method for computing a root to represent a group of identical roots. Default is ‘avg’. See unique_roots for further details.
- Returns:
b (ndarray) – Numerator polynomial coefficients.
a (ndarray) – Denominator polynomial coefficients.
See also