Bilinear transformation method in Signal Processing - Mini Project: Build & Apply

Bilinear Transformation Method

📖 Scenario: You are working as a signal processing engineer. You need to convert an analog filter into a digital filter using the bilinear transformation method. This method helps to map the analog filter's frequency response into the digital domain.

🎯 Goal: Build a Python program that applies the bilinear transformation method to convert an analog filter's transfer function coefficients into digital filter coefficients.

📋 What You'll Learn

Create variables for analog filter numerator and denominator coefficients

Define the sampling frequency

Apply the bilinear transformation using the scipy.signal.bilinear function

Print the resulting digital filter numerator and denominator coefficients

💡 Why This Matters

🌍 Real World

Bilinear transformation is used in designing digital filters from analog prototypes, which is common in audio processing, communications, and control systems.

💼 Career

Understanding bilinear transformation helps engineers convert analog designs to digital implementations, a key skill in signal processing and embedded systems jobs.

1

Create analog filter coefficients

Create two lists called b_analog and a_analog with these exact values: b_analog = [1, 0] and a_analog = [1, 1].

Signal Processing

# Create the analog filter numerator coefficients b_analog and denominator coefficients a_analog
# Your code here

Hint

The numerator and denominator coefficients represent the analog filter's transfer function.

2

Define the sampling frequency

Create a variable called fs and set it to 1000 to represent the sampling frequency in Hertz.

Signal Processing

b_analog = [1, 0]
a_analog = [1, 1]
# Define the sampling frequency fs
# Your code here

Hint

The sampling frequency is how often the digital signal is sampled per second.

3

Apply the bilinear transformation

Import bilinear from scipy.signal. Use bilinear(b_analog, a_analog, fs) to compute the digital filter coefficients. Store the results in variables b_digital and a_digital.

Signal Processing

b_analog = [1, 0]
a_analog = [1, 1]
fs = 1000
# Import bilinear and apply the bilinear transformation
# Your code here

Hint

The bilinear function converts analog coefficients to digital coefficients using the sampling frequency.

4

Print the digital filter coefficients

Print the variables b_digital and a_digital to display the digital filter numerator and denominator coefficients.

Signal Processing

from scipy.signal import bilinear

b_analog = [1, 0]
a_analog = [1, 1]
fs = 1000

b_digital, a_digital = bilinear(b_analog, a_analog, fs)
# Print the digital filter coefficients
# Your code here

Hint

The printed arrays show the digital filter coefficients after transformation.