`scipy.signal._lti_conversion:ss2tf`

source: build-install/usr/lib/python3.14/site-packages/scipy/signal/_lti_conversion.py:236

Signature

def ss2tf(A, B, C, D, input = 0)

Summary

State-space to transfer function.

Extended Summary

A, B, C, D defines a linear state-space system with p inputs, q outputs, and n state variables.

Parameters

A : array_like: State (or system) matrix of shape (n, n)
B : array_like: Input matrix of shape (n, p)
C : array_like: Output matrix of shape (q, n)
D : array_like: Feedthrough (or feedforward) matrix of shape (q, p)
input : int, optional: For multiple-input systems, the index of the input to use.

Returns

num : 2-D ndarray: Numerator(s) of the resulting transfer function(s). num has one row for each of the system's outputs. Each row is a sequence representation of the numerator polynomial.
den : 1-D ndarray: Denominator of the resulting transfer function(s). den is a sequence representation of the denominator polynomial.

Notes

Before calculating num and den, the function abcd_normalize is called to convert the parameters A, B, C, D into two-dimensional arrays of the same dtype. The resulting dtype will be based on NumPy's dtype promotion rules, except in the case where each of A, B, C, and D has integer dtype, in which case the resulting dtype will be the default floating point dtype of float64.

The tutorial_signal_state_space_representation section of the user_guide presents the corresponding definitions of continuous-time and disrcete time state space systems.

Examples

Convert the state-space representation: .. math:: \dot{\textbf{x}}(t) = \begin{bmatrix} -2 & -1 \\ 1 & 0 \end{bmatrix} \textbf{x}(t) + \begin{bmatrix} 1 \\ 0 \end{bmatrix} \textbf{u}(t) \\ \textbf{y}(t) = \begin{bmatrix} 1 & 2 \end{bmatrix} \textbf{x}(t) + \begin{bmatrix} 1 \end{bmatrix} \textbf{u}(t)

A = [[-2, -1], [1, 0]]
B = [[1], [0]]  # 2-D column vector
C = [[1, 2]]    # 2-D row vector
D = 1

✓

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

from scipy.signal import ss2tf

✓

ss2tf(A, B, C, D)

✗

(array([[1., 3., 3.]]), array([1., 2., 1.]))

Aliases

scipy.signal.ss2tf