scipy.signal.invresz¶
-
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.
- parray_like
Poles.
- karray_like
Coefficients of the direct polynomial term.
- tolfloat, optional
The tolerance for two roots to be considered equal. Default is 1e-3.
- rtype{‘max’, ‘min, ‘avg’}, optional
How to determine the returned root if multiple roots are within tol of each other.
‘max’: pick the maximum of those roots.
‘min’: pick the minimum of those roots.
‘avg’: take the average of those roots.
- Returns
- bndarray
Numerator polynomial coefficients.
- andarray
Denominator polynomial coefficients.
See also