lti-arithmetic

Arithmetic manipulation for scipy.signal.lti TransferFunction

LTI system representations in scipy do not offer built-in composability. Given two instances of scipy.signal.lti, for example, H and G, you cannot directly write H * G.

This package defines a scipy.signal.lti-compatible TransferFunction that permits standard arithmetical combination: H + G, H - G, H * G, H / G, and H**n. In addition, the parallel combination (reciprocal of reciprocal sums) of systems is available by writing H | G.

The package also defines functions Z_R, Z_C, and Z_L that represent the impedance of a resistance, capacitance, and inductance, respectively, as LTI systems that can be composed to represent the transfer function of a larger network.

For convenience, the package also defines s so that transfer functions can be written as rational expressions in s.

Examples

>>> from ltiarithmetic import TransferFunction, Z_R, Z_C, Z_L, s

Compute the product of two LTI systems:

>>> H = TransferFunction([1,2,3],[1])
>>> G = TransferFunction[[1],[2,3,4])
>>> H * G
TransferFunction(
array([0.5, 1. , 1.5]),
array([1. , 1.5, 2. ]),
dt: None
)

Compute the transfer function of a RC lowpass filter:

Z_1 = Z_R(1000.)
Z_2 = Z_C(1e-9)
H = Z_2 / (Z_1 + Z_2)

Construct LTI systems from rational expressions in s:

import math
w0 = 2 * math.pi * 1000.
Q = 2.
H = 1/(1 + s / (Q * w0) + (s / w0)**2)