Time shifting a signal in Signal Processing - Mini Project: Build & Apply

Time Shifting a Signal

📖 Scenario: Imagine you have a simple signal represented by a list of numbers. This signal could be a sound wave, a sensor reading, or any data changing over time. Sometimes, you want to shift this signal forward or backward in time to analyze or compare it.

🎯 Goal: You will create a Python program that shifts a signal by a given number of time steps. Positive shifts move the signal forward (delay), and negative shifts move it backward (advance). The empty spaces created by shifting will be filled with zeros.

📋 What You'll Learn

Create a list called signal with exact values: [3, 5, 7, 9, 11]

Create an integer variable called shift_amount with the value 2

Write code to shift the signal by shift_amount steps, filling empty spots with 0

Print the shifted signal list

💡 Why This Matters

🌍 Real World

Time shifting signals is common in audio processing, sensor data analysis, and communications to align or compare signals.

💼 Career

Understanding how to manipulate signals by shifting is a basic skill for data scientists working with time series or signal data.

1

Create the original signal list

Create a list called signal with these exact values: [3, 5, 7, 9, 11]

Signal Processing

# Create the signal list with values [3, 5, 7, 9, 11]
# Your code here

Hint

Use square brackets to create a list and separate numbers with commas.

2

Set the shift amount

Create an integer variable called shift_amount and set it to 2

Signal Processing

signal = [3, 5, 7, 9, 11]
# Create shift_amount variable and set it to 2
# Your code here

Hint

Just assign the number 2 to the variable shift_amount.

3

Shift the signal by the shift amount

Write code to create a new list called shifted_signal that shifts the signal by shift_amount steps forward. Fill empty positions with 0. Use list slicing and concatenation.

Signal Processing

signal = [3, 5, 7, 9, 11]
shift_amount = 2
# Create shifted_signal by shifting signal forward by shift_amount steps
# Fill empty spots with 0
# Your code here

Hint

Use [0]*shift_amount to create zeros and signal[:-shift_amount] to slice the list.

4

Print the shifted signal

Print the shifted_signal list to see the result

Signal Processing

signal = [3, 5, 7, 9, 11]
shift_amount = 2
shifted_signal = [0]*shift_amount + signal[:-shift_amount]
# Print shifted_signal
# Your code here

Hint

Use print(shifted_signal) to display the shifted list.

Practice

1. What does a positive time shift do to a signal in signal processing?

easy

A. It advances the signal, moving it backward in time.

B. It delays the signal, moving it forward in time.

C. It changes the signal's amplitude.

D. It reverses the signal in time.

Solution

1. Step 1: Understand time shift direction

   A positive time shift means the signal is moved to a later time, which delays it.

2. Step 2: Compare options with definition

   Only It delays the signal, moving it forward in time. correctly states that a positive shift delays the signal.

3. Final Answer:

   It delays the signal, moving it forward in time. -> Option B

4. Quick Check:

   Positive shift = delay [OK]

Hint: Positive shift means delay, negative means advance [OK]

Common Mistakes:

• Confusing positive shift with advancing the signal
• Thinking time shift changes amplitude
• Mixing up delay and reversal

2. Which of the following is the correct Python syntax to shift a discrete signal array x by 3 units forward (delay)?

easy

A. shifted_x = np.roll(x, 3)

B. shifted_x = np.roll(x, -3)

C. shifted_x = x + 3

D. shifted_x = x.shift(3)

Solution

1. Step 1: Understand np.roll behavior

   In numpy, np.roll(x, 3) shifts elements to the right by 3, delaying the signal.

2. Step 2: Check other options

   shifted_x = x.shift(3) is invalid syntax for numpy arrays, np.roll(x, -3) shifts left (advances), x + 3 adds 3 to values (not time shift).

3. Final Answer:

   shifted_x = np.roll(x, 3) -> Option A

4. Quick Check:

   np.roll with positive shift delays signal [OK]

Hint: np.roll with positive number delays signal [OK]

Common Mistakes:

• Using negative shift to delay signal
• Adding number to array instead of rolling
• Using non-existent shift method

3. Given the signal array x = [1, 2, 3, 4, 5], what is the output of np.roll(x, -2)?

medium

A. [4, 5, 1, 2, 3]

B. [2, 3, 4, 5, 1]

C. [3, 4, 5, 1, 2]

D. [5, 1, 2, 3, 4]

Solution

1. Step 1: Understand np.roll with negative shift

   Negative shift moves elements to the left by 2 positions.

2. Step 2: Apply shift to array

   Original: [1, 2, 3, 4, 5]
   Shift left 2: [3, 4, 5, 1, 2]

3. Final Answer:

   [3, 4, 5, 1, 2] -> Option C

4. Quick Check:

   Negative shift = advance signal [OK]

Hint: Negative np.roll shifts left (advances) [OK]

Common Mistakes:

• Confusing left and right shift directions
• Miscounting shifted elements
• Assuming shift changes values

4. The following code attempts to shift a signal x = [10, 20, 30, 40] by 1 unit forward but produces incorrect output. What is the error?

shifted_x = np.roll(x, -1)

medium

A. The shift value should be positive to delay the signal.

B. np.roll cannot be used for shifting signals.

C. The array x must be converted to a numpy array first.

D. The shift value should be zero for no change.

Solution

1. Step 1: Analyze shift direction

   Negative shift (-1) moves signal left (advances), not forward (delay).

2. Step 2: Correct shift value

   To delay (shift forward), use positive shift value +1.

3. Final Answer:

   The shift value should be positive to delay the signal. -> Option A

4. Quick Check:

   Positive shift delays signal [OK]

Hint: Positive shift delays; negative advances [OK]

Common Mistakes:

• Using negative shift to delay signal
• Thinking np.roll is invalid for shifting
• Forgetting to convert list to numpy array (not required here)

5. You have two signals sampled at the same rate: s1 = [0, 1, 2, 3, 4] and s2 = [3, 4, 0, 1, 2]. Which time shift applied to s1 aligns it best with s2?

hard

A. Shift s1 by +3 units (delay by 3)

B. Shift s1 by +1 units (delay by 1)

C. Shift s1 by -2 units (advance by 2)

D. Shift s1 by -3 units (advance by 3)

Solution

1. Step 1: Compare signals visually

   s1 = [0, 1, 2, 3, 4], s2 = [3, 4, 0, 1, 2]. s2 matches s1 advanced (shifted left) by 3.

2. Step 2: Verify with np.roll

   np.roll(s1, -3) = [3, 4, 0, 1, 2] matches s2 exactly. np.roll(s1, 1) = [4, 0, 1, 2, 3], np.roll(s1, -2) = [2, 3, 4, 0, 1], np.roll(s1, 3) = [2, 3, 4, 0, 1] do not match.

3. Final Answer:

   Shift s1 by -3 units (advance by 3) -> Option D

4. Quick Check:

   np.roll(s1, -3) == s2 [OK]

Hint: Match s2 by rolling s1 left/right to align [OK]

Common Mistakes:

• Choosing wrong shift direction
• Not checking exact element alignment
• Confusing delay with advance