Common Z-transform pairs in Signal Processing - Mini Project: Build & Apply

Common Z-transform Pairs

📖 Scenario: You are working with digital signals and want to understand how common time-domain sequences relate to their Z-transforms. This helps in analyzing and designing digital filters.

🎯 Goal: Build a Python dictionary of common discrete-time signals and their Z-transform pairs, then filter and display specific pairs based on a condition.

📋 What You'll Learn

Create a dictionary called z_pairs with given time-domain sequences as keys and their Z-transform expressions as values.

Create a variable called filter_key to select a specific time-domain sequence.

Use a dictionary comprehension to create a new dictionary filtered_pairs that contains only the pair matching filter_key.

Print the filtered_pairs dictionary.

💡 Why This Matters

🌍 Real World

Digital signal processing engineers use Z-transform pairs to analyze and design filters and systems that work with discrete signals.

💼 Career

Understanding Z-transform pairs is essential for roles in signal processing, communications, and control systems engineering.

1

Create the Z-transform pairs dictionary

Create a dictionary called z_pairs with these exact entries: 'delta[n]': '1', 'u[n]': '1 / (1 - z^-1)', 'a^n u[n]': '1 / (1 - a z^-1)', 'n u[n]': 'z^-1 / (1 - z^-1)^2'.

Signal Processing

# Create the dictionary z_pairs with the given time-domain sequences and their Z-transforms
# Your code here

Hint

Use curly braces {} to create the dictionary and separate each key-value pair with a comma.

2

Set the filter key

Create a variable called filter_key and set it to the string 'a^n u[n]'.

Signal Processing

z_pairs = {
    'delta[n]': '1',
    'u[n]': '1 / (1 - z^-1)',
    'a^n u[n]': '1 / (1 - a z^-1)',
    'n u[n]': 'z^-1 / (1 - z^-1)^2'
}
# Create the variable filter_key with the value 'a^n u[n]'
# Your code here

Hint

Assign the string 'a^n u[n]' to the variable filter_key.

3

Filter the dictionary using comprehension

Use a dictionary comprehension to create a new dictionary called filtered_pairs that contains only the key-value pair from z_pairs where the key matches filter_key.

Signal Processing

z_pairs = {
    'delta[n]': '1',
    'u[n]': '1 / (1 - z^-1)',
    'a^n u[n]': '1 / (1 - a z^-1)',
    'n u[n]': 'z^-1 / (1 - z^-1)^2'
}
filter_key = 'a^n u[n]'
# Create filtered_pairs using dictionary comprehension
# Your code here

Hint

Use {k: v for k, v in z_pairs.items() if k == filter_key} to filter the dictionary.

4

Print the filtered dictionary

Print the variable filtered_pairs to display the filtered Z-transform pair.

Signal Processing

z_pairs = {
    'delta[n]': '1',
    'u[n]': '1 / (1 - z^-1)',
    'a^n u[n]': '1 / (1 - a z^-1)',
    'n u[n]': 'z^-1 / (1 - z^-1)^2'
}
filter_key = 'a^n u[n]'
filtered_pairs = {k: v for k, v in z_pairs.items() if k == filter_key}
# Print the filtered_pairs dictionary
# Your code here

Hint

Use print(filtered_pairs) to display the result.