invresz — SciPy v1.15.3 Manual (original) (raw)

scipy.signal.

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:

rarray_like

Residues corresponding to the poles. For repeated poles, the residues must be ordered to correspond to ascending by power fractions.

parray_like

Poles. Equal poles must be adjacent.

karray_like

Coefficients of the direct polynomial term.

tolfloat, optional

The tolerance for two roots to be considered equal in terms of the distance between them. Default is 1e-3. See unique_rootsfor 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:

bndarray

Numerator polynomial coefficients.

andarray

Denominator polynomial coefficients.