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

scipy.signal.

scipy.signal.invres(r, p, k, tol=0.001, rtype='avg')[source]#

Compute b(s) and a(s) from partial fraction expansion.

If M is the degree of numerator b and N the degree of denominator_a_:

    b(s)     b[0] s**(M) + b[1] s**(M-1) + ... + b[M]

H(s) = ------ = ------------------------------------------ a(s) a[0] s**(N) + a[1] s**(N-1) + ... + a[N]

then the partial-fraction expansion H(s) is defined as:

r[0]       r[1]             r[-1]

= -------- + -------- + ... + --------- + k(s) (s-p[0]) (s-p[1]) (s-p[-1])

If there are any repeated roots (closer together than tol), then H(s) has terms like:

r[i] r[i+1] r[i+n-1] -------- + ----------- + ... + ----------- (s-p[i]) (s-p[i])**2 (s-p[i])**n

This function is used for polynomials in positive powers of s or z, such as analog filters or digital filters in controls engineering. For negative powers of z (typical for digital filters in DSP), use invresz.

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.