scipy.signal.

dfreqresp#

scipy.signal.dfreqresp(system, w=None, n=10000, whole=False)[source]#

Calculate the frequency response of a discrete-time system.

Parameters:

systemdlti | tuple

An instance of the LTI class dlti or a tuple describing the system. The number of elements in the tuple determine the interpretation. I.e.:

system: Instance of LTI class dlti. Note that derived instances, such as instances of TransferFunction, ZerosPolesGain, or StateSpace, are allowed as well.
(num, den, dt): Rational polynomial as described in TransferFunction. The coefficients of the polynomials should be specified in descending exponent order, e.g., z² + 3z + 5 would be represented as [1, 3, 5].
(zeros, poles, gain, dt): Zeros, poles, gain form as described in ZerosPolesGain.
(A, B, C, D, dt): State-space form as described in StateSpace.

warray_like, optional

Array of frequencies (in radians/sample). Magnitude and phase data is calculated for every value in this array. If not given a reasonable set will be calculated.

nint, optional

Number of frequency points to compute if w is not given. The n frequencies are logarithmically spaced in an interval chosen to include the influence of the poles and zeros of the system.

wholebool, optional

Normally, if ‘w’ is not given, frequencies are computed from 0 to the Nyquist frequency, pi radians/sample (upper-half of unit-circle). If whole is True, compute frequencies from 0 to 2*pi radians/sample.

Returns:

w1D ndarray: Frequency array [radians/sample]
H1D ndarray: Array of complex magnitude values

Notes

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

Added in version 0.18.0.

Examples

The following example generates the Nyquist plot of the transfer function \(H(z) = \frac{1}{z^2 + 2z + 3}\) with a sampling time of 0.05 seconds:

>>> from scipy import signal
>>> import matplotlib.pyplot as plt
>>> sys = signal.TransferFunction([1], [1, 2, 3], dt=0.05)  # construct H(z)
>>> w, H = signal.dfreqresp(sys)
...
>>> fig0, ax0 = plt.subplots()
>>> ax0.plot(H.real, H.imag, label=r"$H(z=e^{+j\omega})$")
>>> ax0.plot(H.real, -H.imag, label=r"$H(z=e^{-j\omega})$")
>>> ax0.set_title(r"Nyquist Plot of $H(z) = 1 / (z^2 + 2z + 3)$")
>>> ax0.set(xlabel=r"$\text{Re}\{z\}$", ylabel=r"$\text{Im}\{z\}$",
...         xlim=(-0.2, 0.65), aspect='equal')
>>> ax0.plot(H[0].real, H[0].imag, 'k.')  # mark H(exp(1j*w[0]))
>>> ax0.text(0.2, 0, r"$H(e^{j0})$")
>>> ax0.grid(True)
>>> ax0.legend()
>>> plt.show()

../../_images/scipy-signal-dfreqresp-1.png