scipy.signal.freqz

scipy.signal.freqz(b, a=1, worN=None, whole=0, plot=None)

Compute the frequency response of a digital filter.

Given the numerator b and denominator a of a digital filter compute its frequency response:

          jw               -jw            -jmw
   jw  B(e)    b[0] + b[1]e + .... + b[m]e
H(e) = ---- = ------------------------------------
          jw               -jw            -jnw
       A(e)    a[0] + a[1]e + .... + a[n]e

Parameters :

b : ndarray

numerator of a linear filter

a : ndarray

numerator of a linear filter

worN : {None, int}, optional

If None, then compute at 512 frequencies around the unit circle. If a single integer, the compute at that many frequencies. Otherwise, compute the response at frequencies given in worN

whole : {0,1}, optional

Normally, frequencies are computed from 0 to pi (upper-half of unit-circle. If whole is non-zero compute frequencies from 0 to 2*pi.

Returns :

w : ndarray

The frequencies at which h was computed.

h : ndarray

The frequency response.

Examples

>>> b = firwin(80, 0.5, window=('kaiser', 8))
>>> h, w = freqz(b)

>>> import matplotlib.pyplot as plt
>>> fig = plt.figure()
>>> plt.title('Digital filter frequency response')
>>> ax1 = fig.add_subplot(111)

>>> plt.semilogy(h, np.abs(w), 'b')
>>> plt.ylabel('Amplitude (dB)', color='b')
>>> plt.xlabel('Frequency (rad/sample)')
>>> plt.grid()
>>> plt.legend()

>>> ax2 = ax1.twinx()
>>> angles = np.unwrap(np.angle(w))
>>> plt.plot(h, angles, 'g')
>>> plt.ylabel('Angle (radians)', color='g')
>>> plt.show()