Time shifting a signal in Signal Processing - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to shift the signal x by 3 units to the right.

Signal Processing

import numpy as np
x = np.array([1, 2, 3, 4, 5])
shifted_x = np.roll(x, [1])
print(shifted_x)

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

A3

B0

C-3

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using negative shift value which shifts left instead of right.

Using zero which does not shift the signal.

Using np.roll with 3 shifts the array elements 3 places to the right.

2fill in blank

medium

Complete the code to shift the signal x by 2 units to the left.

Signal Processing

import numpy as np
x = np.array([10, 20, 30, 40, 50])
shifted_x = np.roll(x, [1])
print(shifted_x)

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

A1

B2

C0

D-2

Attempts:

3 left

💡 Hint

Common Mistakes

Using positive shift value which shifts right instead of left.

Using zero which does not shift the signal.

Using np.roll with -2 shifts the array elements 2 places to the left.

3fill in blank

hard

Fix the error in the code to shift the signal x by 1 unit to the right.

Signal Processing

import numpy as np
x = [5, 10, 15, 20]
shifted_x = np.roll([1], 1)
print(shifted_x)

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

Anp.array(x)

Bx.tolist()

Clist(x)

Dx

Attempts:

3 left

💡 Hint

Common Mistakes

Passing a Python list directly to np.roll causes unexpected behavior.

Using list conversion methods that do not convert to numpy array.

np.roll requires a numpy array, so convert the list x to an array first.

4fill in blank

hard

Fill both blanks to create a time-shifted signal by 2 units to the left and then multiply by 2.

Signal Processing

import numpy as np
x = np.array([1, 3, 5, 7, 9])
shifted_x = np.roll(x, [1]) * [2]
print(shifted_x)

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

A-2

B2

C3

D1

Attempts:

3 left

💡 Hint

Common Mistakes

Using positive shift value which shifts right instead of left.

Multiplying by 1 which does not change the signal.

Shift left by 2 using -2, then multiply the shifted signal by 2.

5fill in blank

hard

Fill all three blanks to create a shifted signal by 1 unit right, then add 5 to each element, and finally divide by 2.

Signal Processing

import numpy as np
x = np.array([2, 4, 6, 8, 10])
result = (np.roll(x, [1]) + [2]) / [3]
print(result)

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

A1

B5

C2

D3

Attempts:

3 left

💡 Hint

Common Mistakes

Using negative shift which moves signal left.

Adding or dividing by wrong numbers causing incorrect results.

Shift right by 1, add 5 to each element, then divide the result by 2.

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