Bilinear transformation method in Signal Processing - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to import the function used for bilinear transformation from scipy.signal.

Signal Processing

from scipy.signal import [1]

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Afft

Bbilinear

Cconvolve

Dlfilter

Attempts:

3 left

💡 Hint

Common Mistakes

Importing unrelated functions like fft or convolve.

Using lfilter which is for filtering signals, not transformation.

The bilinear function from scipy.signal is used to perform the bilinear transformation.

2fill in blank

medium

Complete the code to define the analog filter numerator coefficients as a list.

Signal Processing

b = [1]

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A1, 0

B(1, 0)

C[1, 0]

D{1, 0}

Attempts:

3 left

💡 Hint

Common Mistakes

Using tuples or sets instead of lists.

Not enclosing coefficients in any brackets.

Filter coefficients should be defined as a list of numbers, e.g., [1, 0].

3fill in blank

hard

Fix the error in the code to correctly perform the bilinear transformation.

Signal Processing

b_z, a_z = bilinear(b, [1], fs)

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A1

Bb

Cfs

Da

Attempts:

3 left

💡 Hint

Common Mistakes

Passing numerator coefficients twice.

Passing sampling frequency as the second argument.

The second argument to bilinear is the denominator coefficients a of the analog filter.

4fill in blank

hard

Fill both blanks to define the sampling frequency and apply bilinear transform correctly.

Signal Processing

fs = [1]
b_z, a_z = bilinear(b, a, [2])

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A1000

B500

Cfs

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using incorrect sampling frequency values.

Passing a literal number instead of the variable fs.

The sampling frequency fs is set to 1000 Hz, and then passed as the third argument to bilinear.

5fill in blank

hard

Fill all three blanks to create a digital filter using bilinear transform and print the numerator coefficients.

Signal Processing

b = [1]
a = [2]
fs = 2000
b_z, a_z = bilinear(b, a, [3])
print(b_z)

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A[0.0675, 0.1349, 0.0675]

B[1, -1.143, 0.4128]

Cfs

D[1, 0.5, 0.25]

Attempts:

3 left

💡 Hint

Common Mistakes

Mixing up numerator and denominator coefficients.

Passing sampling frequency as a list or wrong variable.

Not printing the correct variable.

The analog filter numerator b and denominator a coefficients are defined as lists. The sampling frequency fs is passed to bilinear. The output b_z contains the digital filter numerator coefficients.