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Module « scipy.signal »

Fonction tf2zpk - module scipy.signal

Signature de la fonction tf2zpk

def tf2zpk(b, a) 

Description

help(scipy.signal.tf2zpk)

Return zero, pole, gain (z, p, k) representation from a numerator,
denominator representation of a linear filter.

Parameters
----------
b : array_like
    Numerator polynomial coefficients.
a : array_like
    Denominator polynomial coefficients.

Returns
-------
z : ndarray
    Zeros of the transfer function.
p : ndarray
    Poles of the transfer function.
k : float
    System gain.

Notes
-----
If some values of `b` are too close to 0, they are removed. In that case,
a BadCoefficients warning is emitted.

The `b` and `a` arrays are interpreted as coefficients for positive,
descending powers of the transfer function variable. So the inputs
:math:`b = [b_0, b_1, ..., b_M]` and :math:`a =[a_0, a_1, ..., a_N]`
can represent an analog filter of the form:

.. math::

    H(s) = \frac
    {b_0 s^M + b_1 s^{(M-1)} + \cdots + b_M}
    {a_0 s^N + a_1 s^{(N-1)} + \cdots + a_N}

or a discrete-time filter of the form:

.. math::

    H(z) = \frac
    {b_0 z^M + b_1 z^{(M-1)} + \cdots + b_M}
    {a_0 z^N + a_1 z^{(N-1)} + \cdots + a_N}

This "positive powers" form is found more commonly in controls
engineering. If `M` and `N` are equal (which is true for all filters
generated by the bilinear transform), then this happens to be equivalent
to the "negative powers" discrete-time form preferred in DSP:

.. math::

    H(z) = \frac
    {b_0 + b_1 z^{-1} + \cdots + b_M z^{-M}}
    {a_0 + a_1 z^{-1} + \cdots + a_N z^{-N}}

Although this is true for common filters, remember that this is not true
in the general case. If `M` and `N` are not equal, the discrete-time
transfer function coefficients must first be converted to the "positive
powers" form before finding the poles and zeros.

Examples
--------
Find the zeroes, poles and gain of
a filter with the transfer function

.. math::

    H(s) = \frac{3s^2}{s^2 + 5s + 13}

>>> from scipy.signal import tf2zpk
>>> tf2zpk([3, 0, 0], [1, 5, 13])
(   array([ 0.               ,  0.              ]),
    array([ -2.5+2.59807621j ,  -2.5-2.59807621j]),
    3.0)

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