Transfer function H(z) in Signal Processing - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to define the transfer function H(z) using numerator and denominator coefficients.

Signal Processing

from scipy.signal import TransferFunction
num = [1, -0.5]
den = [1, -0.9]
H = TransferFunction([1], den, dt=1)

Drag options to blanks, or click blank then click option'

Aden

B[0.5, 1]

C[1, 0]

Dnum

Attempts:

3 left

💡 Hint

Common Mistakes

Using denominator coefficients instead of numerator.

Passing a wrong list of coefficients.

The numerator coefficients are stored in num, which define the zeros of the transfer function H(z).

2fill in blank

medium

Complete the code to compute the frequency response of H(z) at 512 points.

Signal Processing

from scipy.signal import freqz
w, h = freqz(H.num, H.den, worN=[1])

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A1024

B128

C512

D256

Attempts:

3 left

💡 Hint

Common Mistakes

Using too few points leading to rough plots.

Using a non-integer or invalid value.

512 points is a common choice for smooth frequency response plots.

3fill in blank

hard

Fix the error in the code to correctly calculate the magnitude response in decibels.

Signal Processing

import numpy as np
magnitude_db = 20 * np.log10([1])

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Aabs(h)

Bh

Cnp.abs(h)**2

Dnp.log10(h)

Attempts:

3 left

💡 Hint

Common Mistakes

Using h directly without absolute value.

Squaring magnitude before log10 incorrectly.

The magnitude must be the absolute value of h before applying log10.

4fill in blank

hard

Fill both blanks to create a dictionary of frequency response with frequency in Hz and magnitude in dB.

Signal Processing

freq_response = [1]: w * [2] / (2 * np.pi) for w, mag in zip(w, magnitude_db)

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A{'frequency_hz'

Bfs

C1

Dnp.pi

Attempts:

3 left

💡 Hint

Common Mistakes

Using wrong dictionary key names.

Incorrect frequency scaling factor.

The dictionary key is 'frequency_hz' and frequency is scaled by sampling frequency fs.

5fill in blank

hard

Fill all three blanks to filter a signal x using the transfer function H and store the output in y.

Signal Processing

from scipy.signal import lfilter
y = lfilter([1], [2], [3])

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AH.num

BH.den

Cx

DH

Attempts:

3 left

💡 Hint

Common Mistakes

Passing the transfer function object instead of coefficients.

Swapping numerator and denominator coefficients.

The lfilter function takes numerator coefficients, denominator coefficients, and the input signal.