`scipy.signal._ltisys:TransferFunction`

source: /scipy/signal/_ltisys.py :494

Signature

class TransferFunction ( * system , ** kwargs )

Members

Summary

Linear Time Invariant system class in transfer function form.

Extended Summary

Represents the system as the continuous-time transfer function $H (s) = \sum_{i = 0}^{N} b [N - i] s^{i} / \sum_{j = 0}^{M} a [M - j] s^{j}$ or the discrete-time transfer function $H (z) = \sum_{i = 0}^{N} b [N - i] z^{i} / \sum_{j = 0}^{M} a [M - j] z^{j}$ , where $b$ are elements of the numerator num, $a$ are elements of the denominator den, and N == len(b) - 1, M == len(a) - 1. TransferFunction systems inherit additional functionality from the lti, respectively the dlti classes, depending on which system representation is used.

Parameters

*system: arguments

The TransferFunction class can be instantiated with 1 or 2 arguments. The following gives the number of input arguments and their interpretation:

1: lti or dlti system: (StateSpace, TransferFunction or ZerosPolesGain)
2: array_like: (numerator, denominator)

dt: float, optional

Sampling time [s] of the discrete-time systems. Defaults to None (continuous-time). Must be specified as a keyword argument, for example, dt=0.1.

Notes

Changing the value of properties that are not part of the TransferFunction system representation (such as the A, B, C, D state-space matrices) is very inefficient and may lead to numerical inaccuracies. It is better to convert to the specific system representation first. For example, call sys = sys.to_ss() before accessing/changing the A, B, C, D system matrices.

If (numerator, denominator) is passed in for *system, coefficients for both the numerator and denominator should be specified in descending exponent order (e.g. s^2 + 3s + 5 or z^2 + 3z + 5 would be represented as [1, 3, 5])

Array API Standard Support

TransferFunction has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

====================  ====================  ====================
Library               CPU                   GPU
====================  ====================  ====================
NumPy                 ✅                     n/a                 
CuPy                  n/a                   ⛔                   
PyTorch               ⛔                     ⛔                   
JAX                   ⛔                     ⛔                   
Dask                  ⛔                     n/a                 
====================  ====================  ====================

See dev-arrayapi for more information.

Examples

Construct the transfer function :math:`H(s) = \frac{s^2 + 3s + 3}{s^2 + 2s + 1}`:

from scipy import signal

✓

num = [1, 3, 3]
den = [1, 2, 1]

✓

signal.TransferFunction(num, den)

✓

Construct the transfer function :math:`H(z) = \frac{z^2 + 3z + 3}{z^2 + 2z + 1}` with a sampling time of 0.1 seconds:

signal.TransferFunction(num, den, dt=0.1)

✓

Aliases

scipy.signal.TransferFunction