Echo and reverb effects in Signal Processing - Interactive Code Practice

Practice - 5 Tasks

1fill in blank

easy

Complete the code to create a delayed echo by adding the original signal to a delayed version.

Signal Processing

echo_signal = original_signal + [1]

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

Anp.zeros_like(original_signal)

Boriginal_signal * delay_samples

Coriginal_signal - delay_samples

Dnp.roll(original_signal, delay_samples)

Attempts:

3 left

💡 Hint

Common Mistakes

Multiplying the signal by delay_samples instead of shifting it.

Subtracting delay_samples from the signal, which is invalid.

Using zeros instead of a delayed signal.

We use np.roll to shift the signal by delay_samples, creating the delayed echo.

2fill in blank

medium

Complete the code to apply a decay factor to the delayed echo signal.

Signal Processing

echo_signal = original_signal + [1] * np.roll(original_signal, delay_samples)

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

A1.5

Bdecay

Cdelay_samples

Doriginal_signal

Attempts:

3 left

💡 Hint

Common Mistakes

Using the delay_samples as decay, which is incorrect.

Using a value greater than 1, which amplifies instead of decays.

Multiplying by the original signal again instead of decay.

The decay factor reduces the amplitude of the delayed echo to simulate fading.

3fill in blank

hard

Fix the error in the code to correctly create a reverb effect by summing multiple delayed signals with decay.

Signal Processing

reverb_signal = original_signal
for i in range(1, num_echoes):
    reverb_signal += [1] * np.roll(original_signal, i * delay_samples)

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

Adecay ** i

Bdecay * i

Ci ** decay

Ddecay + i

Attempts:

3 left

💡 Hint

Common Mistakes

Multiplying decay by i instead of using exponential decay.

Adding decay and i, which does not reduce amplitude properly.

Raising i to the power of decay, which reverses the intended effect.

Decay should be raised to the power of i to reduce amplitude exponentially for each echo.

4fill in blank

hard

Fill both blanks to create a dictionary comprehension that maps each echo number to its delayed and decayed signal.

Signal Processing

echoes = {i: [1] * np.roll(original_signal, i * [2]) for i in range(1, num_echoes)}

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

Adecay ** i

Bdelay_samples

Cdecay * i

Dnum_echoes

Attempts:

3 left

💡 Hint

Common Mistakes

Using linear decay instead of exponential decay.

Using num_echoes as delay, which is incorrect.

Mixing up decay and delay variables.

Each echo is delayed by delay_samples times i and decayed exponentially by decay ** i.

5fill in blank

hard

Fill all three blanks to combine all echoes into a single reverb signal using sum and dictionary comprehension.

Signal Processing

reverb_signal = original_signal + sum([1]: [2] * np.roll(original_signal, [3] * delay_samples) for [1] in range(1, num_echoes)})

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

Ai

Bdecay ** i

Dnum_echoes

Attempts:

3 left

💡 Hint

Common Mistakes

Using different variable names inconsistently.

Not raising decay to the power of i.

Using num_echoes as the delay multiplier.

We sum over i from 1 to num_echoes, applying exponential decay and delay for each echo.

Practice

1. What is the main difference between echo and reverb effects in audio processing?

easy

A. Echo is a single delayed repeat; reverb is many quick repeats.

B. Echo is louder than the original sound; reverb is quieter.

C. Echo removes the original sound; reverb enhances it.

D. Echo happens instantly; reverb has a long delay.

Solution

1. Step 1: Understand echo effect

   Echo is created by adding a single delayed repeat of the original sound.

2. Step 2: Understand reverb effect

   Reverb is created by adding many quick, overlapping repeats that simulate space.

3. Final Answer:

   Echo is a single delayed repeat; reverb is many quick repeats. -> Option A

4. Quick Check:

   Echo vs Reverb difference = single vs many repeats [OK]

Hint: Echo = one delay; reverb = many quick delays [OK]

Common Mistakes:

• Confusing echo with reverb as the same effect
• Thinking echo is louder than original
• Believing reverb removes original sound

2. Which of the following Python code snippets correctly applies a simple echo effect to an audio signal array signal with delay d and decay factor alpha?

easy

A. echoed = signal * alpha + np.roll(signal, d)

B. echoed = signal + alpha * np.roll(signal, d)

C. echoed = np.roll(signal, d) + alpha

D. echoed = signal + np.roll(signal, alpha)

Solution

1. Step 1: Understand echo formula

   Echo effect adds the original signal plus a delayed, scaled copy: signal + alpha * delayed_signal.

2. Step 2: Check code correctness

   echoed = signal + alpha * np.roll(signal, d) uses np.roll(signal, d) to delay and multiplies by alpha, then adds to original signal correctly.

3. Final Answer:

   echoed = signal + alpha * np.roll(signal, d) -> Option B

4. Quick Check:

   Correct echo formula = original + alpha * delayed [OK]

Hint: Echo = original + alpha * delayed signal [OK]

Common Mistakes:

• Multiplying original signal by alpha instead of delayed
• Using alpha as delay index
• Adding alpha as a scalar instead of scaling delayed signal

3. Given the following Python code applying a simple echo effect, what will be the value of output[3]?

import numpy as np
signal = np.array([1, 2, 3, 4, 5])
delay = 2
alpha = 0.5
output = signal + alpha * np.roll(signal, delay)

medium

A. 5.0

B. 4.5

C. 3.5

D. 2.5

Solution

1. Step 1: Calculate delayed signal at index 3

   np.roll(signal, 2) shifts signal by 2: [4, 5, 1, 2, 3]. At index 3, delayed value is 2.

2. Step 2: Calculate output at index 3

   output[3] = signal[3] + alpha * delayed[3] = 4 + 0.5 * 2 = 4 + 1 = 5.0

3. Final Answer:

   5.0 -> Option A

4. Quick Check:

   4 + 0.5*2 = 5.0 [OK]

Hint: Add original + alpha * delayed at index [OK]

Common Mistakes:

• Mixing up indices after roll
• Forgetting to multiply delayed by alpha
• Using wrong delay value

4. The following code attempts to create a reverb effect by mixing multiple delayed signals, but it produces unrealistic results. What is the main issue?

import numpy as np
signal = np.array([1, 2, 3, 4, 5])
delays = [1, 2, 3]
alpha = 0.5
output = signal
for d in delays:
    output += alpha * np.roll(signal, d)

medium

A. The variable output is not initialized as a float array, causing type errors.

B. The += operator cannot be used with numpy arrays.

C. The loop should multiply alpha by d, not signal.

D. Using np.roll shifts the signal incorrectly for reverb.

Solution

1. Step 1: Identify the issue with np.roll

   np.roll(signal, d) performs a circular shift, wrapping the end of the signal to the start, which creates unrealistic artifacts in reverb simulation.

2. Step 2: Proper approach for reverb delays

   To simulate true delays, pad the signal with zeros instead of using circular roll to avoid wrap-around.

3. Final Answer:

   Using np.roll shifts the signal incorrectly for reverb. -> Option D

4. Quick Check:

   np.roll = circular shift [unsuitable for reverb] [OK]

Hint: np.roll wraps around; use zero-padding for delays [OK]

Common Mistakes:

• Using circular np.roll for linear delays
• Ignoring wrap-around artifacts in reverb
• Thinking data types cause issues

5. You want to create a reverb effect by mixing the original audio signal with 3 delayed copies at delays 1, 2, and 3 samples, each with decreasing decay factors 0.6, 0.3, and 0.1 respectively. Which Python code correctly implements this?

hard

A. output = signal + 0.1*np.roll(signal,1) + 0.3*np.roll(signal,2) + 0.6*np.roll(signal,3)

B. output = signal * (0.6 + 0.3 + 0.1) + np.roll(signal,1) + np.roll(signal,2) + np.roll(signal,3)

C. output = signal + 0.6*np.roll(signal,1) + 0.3*np.roll(signal,2) + 0.1*np.roll(signal,3)

D. output = signal + np.roll(signal,1)*0.1 + np.roll(signal,2)*0.3 + np.roll(signal,3)*0.6

Solution

1. Step 1: Understand reverb mixing

   Reverb mixes original plus delayed signals scaled by decay factors in order of delay.

2. Step 2: Match decay factors to delays

   Decay 0.6 for delay 1, 0.3 for delay 2, 0.1 for delay 3 matches output = signal + 0.6*np.roll(signal,1) + 0.3*np.roll(signal,2) + 0.1*np.roll(signal,3).

3. Step 3: Check code correctness

   output = signal + 0.6*np.roll(signal,1) + 0.3*np.roll(signal,2) + 0.1*np.roll(signal,3) adds original signal plus each delayed signal multiplied by correct decay factor.

4. Final Answer:

   output = signal + 0.6*np.roll(signal,1) + 0.3*np.roll(signal,2) + 0.1*np.roll(signal,3) -> Option C

5. Quick Check:

   Decay factors match delays in order [OK]

Hint: Match decay factors to delays in order when adding [OK]

Common Mistakes:

• Mixing decay factors with wrong delays
• Multiplying original signal by sum of decays
• Reversing decay order