scipy.signal.

lp2lp#

scipy.signal.lp2lp(b, a, wo=1.0)[source]#

Transform a lowpass filter prototype to a different frequency.

Return an analog low-pass filter with cutoff frequency wo from an analog low-pass filter prototype with unity cutoff frequency, in transfer function (‘ba’) representation.

Parameters:

barray_like: Numerator polynomial coefficients.
aarray_like: Denominator polynomial coefficients.
wofloat: Desired cutoff, as angular frequency (e.g. rad/s). Defaults to no change.

Returns:

barray_like: Numerator polynomial coefficients of the transformed low-pass filter.
aarray_like: Denominator polynomial coefficients of the transformed low-pass filter.

See also

lp2hp, lp2bp, lp2bs, bilinear
lp2lp_zpk

Notes

This is derived from the s-plane substitution

\[s \rightarrow \frac{s}{\omega_0}\]

Examples

>>> from scipy import signal
>>> import matplotlib.pyplot as plt

>>> lp = signal.lti([1.0], [1.0, 1.0])
>>> lp2 = signal.lti(*signal.lp2lp(lp.num, lp.den, 2))
>>> w, mag_lp, p_lp = lp.bode()
>>> w, mag_lp2, p_lp2 = lp2.bode(w)

>>> plt.plot(w, mag_lp, label='Lowpass')
>>> plt.plot(w, mag_lp2, label='Transformed Lowpass')
>>> plt.semilogx()
>>> plt.grid(True)
>>> plt.xlabel('Frequency [rad/s]')
>>> plt.ylabel('Amplitude [dB]')
>>> plt.legend()