IN PYTHON JUPYTER NOTEBOOK: The scipy library of matplotlib in Python 3 contains

Question

IN PYTHON JUPYTER NOTEBOOK:

The scipy library of matplotlib in Python 3 contains a function "scipy.signal.freqz" which computes the frequency response of a digital filter. I am trying to write my own version of this function, to relay the same output as this imbedded function. I plan to use the inputs: freqz(b, a = 1, worN=None, whole=None): [b=numerator of linear filter; a=denominator of linear filter; worN=at none, compute at 512 frequencies equally spaced around the unit circle; whole=at none, frequency computed around upper half of unit circle, from 0 to pi]. This function should output two outputs: w and h

After implementing the function, it should pass all the tests provided in the last part of code. Need to implement scipy.signal.freqz using different ways other than source code and FFT.

DON'T USE FFT FUNCTION

I am going to provide the code that I am given.

Code:

import numpy as np
import matplotlib.pyplot as plt
import scipy.signal as sig
import matplotlib as mpl
mpl.rcParams['figure.figsize'] = (5,3)
%matplotlib inline

# Implementation of freqz using different way.

Please use the same variables

def my_freqz(b, a = 1, worN=None, whole=None):
#replace with your answer
pass

Testing code:

from collections import namedtuple
Test = namedtuple('Test',['b','a','worN','whole'])
tests = [ Test([1,0.5,0.1], [1,1], 256, None),
Test(1,1,None, True),
Test(1,1,12, False),
Test([1,2],1,[0,1,2,3], None) ]

b,a = sig.iirdesign(0.2, 0.3, 1, 20)
tests.append(Test(b,a,None,None))

b = sig.firwin(63, 0.25)
tests.append(Test(b,1,1024,None))

for test in tests:
w, h = sig.freqz(test.b, test.a, test.worN, test.whole)
my_w, my_h = my_freqz(test.b, test.a, test.worN, test.whole)
print(np.allclose(w, my_w), np.allclose(h, my_h))

Tests should output TRUE for all.

Output should look like

True True

True True

True True

True True

Explanation / Answer

import numpy as np
import matplotlib.pyplot as plt
import scipy.signal as sig
import matplotlib as mpl
mpl.rcParams['figure.figsize'] = (5,3)
%matplotlib inline

def my_freqz(b, a = 1, worN=None, whole=None):

Testing code:
from collections import namedtuple
Test = namedtuple('Test',['b','a','worN','whole'])
tests = [ Test([1,0.5,0.1], [1,1], 256, None),
Test(1,1,None, True),
Test(1,1,12, False),
Test([1,2],1,[0,1,2,3], None) ]
b,a = sig.iirdesign(0.2, 0.3, 1, 20)
tests.append(Test(b,a,None,None))
b = sig.firwin(63, 0.25)
tests.append(Test(b,1,1024,None))
for test in tests:
w, h = sig.freqz(test.b, test.a, test.worN, test.whole)
my_w, my_h = my_freqz(test.b, test.a, test.worN, test.whole)
print(np.allclose(w, my_w), np.allclose(h, my_h))

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