Pitch detection algorithm in Signal Processing - Practice Problems & Coding Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Output of autocorrelation pitch detection snippet

Given the following Python code snippet that computes the autocorrelation of a signal segment to detect pitch, what is the output array?

Signal Processing

import numpy as np
signal = np.array([0, 1, 0, -1, 0, 1, 0, -1])
autocorr = np.correlate(signal, signal, mode='full')
result = autocorr[autocorr.size // 2:]
print(result)

A [4 0 -2 0 1 0 0 0]

B [4 0 -3 0 2 0 -1 0]

C [4 0 -2 0 0 0 0 0]

D [4 0 -3 0 1 0 -1 0]

💡 Hint

Recall that autocorrelation at lag 0 is the sum of squares of the signal values.

The autocorrelation of the signal at lag 0 is 4 (sum of squares). The subsequent values are computed by shifting the signal and summing the product of overlapping elements. Option B matches the correct autocorrelation values.

❓ data_output

intermediate

Number of detected pitch periods in a signal

A pitch detection algorithm segments a 1-second audio sampled at 8000 Hz into frames of 80 samples each. If the algorithm detects a pitch period every frame, how many pitch periods are detected in total?

A 100

B 160

C 125

D 80

💡 Hint

Divide total samples by frame size to find number of frames.

Total samples = 8000. Frame size = 80 samples. Number of frames = 8000 / 80 = 100. Each frame detects one pitch period, so total is 100.

❓ visualization

advanced

Identify correct pitch contour plot

Which plot correctly shows a pitch contour that rises linearly from 100 Hz to 200 Hz over 1 second?

Signal Processing

import matplotlib.pyplot as plt
import numpy as np

time = np.linspace(0, 1, 100)
contour_A = 100 + 100 * time
contour_B = 200 - 100 * time
contour_C = 100 * np.sin(2 * np.pi * time) + 150
contour_D = np.full_like(time, 150)

plt.figure(figsize=(8, 4))
plt.plot(time, contour_A, label='A')
plt.plot(time, contour_B, label='B')
plt.plot(time, contour_C, label='C')
plt.plot(time, contour_D, label='D')
plt.legend()
plt.xlabel('Time (s)')
plt.ylabel('Frequency (Hz)')
plt.title('Pitch Contours')
plt.show()

A Plot B: frequency decreases linearly from 200 to 100 Hz

B Plot C: frequency oscillates sinusoidally around 150 Hz

C Plot A: frequency increases linearly from 100 to 200 Hz

D Plot D: frequency remains constant at 150 Hz

💡 Hint

Look for a straight line increasing from 100 to 200 Hz.

Plot A shows a linear increase from 100 Hz to 200 Hz over 1 second, matching the description of the pitch contour.

🧠 Conceptual

advanced

Effect of window size on pitch detection accuracy

How does increasing the window size in a pitch detection algorithm typically affect the accuracy and time resolution of pitch estimation?

A Decreases accuracy and decreases time resolution

B Increases accuracy and increases time resolution

C Decreases accuracy but increases time resolution

D Increases accuracy but decreases time resolution

💡 Hint

Think about the trade-off between frequency precision and temporal precision.

A larger window size captures more data, improving frequency resolution (accuracy) but reduces the ability to detect quick changes in pitch (time resolution).

🔧 Debug

expert

Identify error in pitch detection code snippet

What error will the following Python code raise when trying to detect pitch using zero crossing rate?

Signal Processing

import numpy as np
signal = np.array([1, -1, 1, -1, 1])
zero_crossings = np.where(np.diff(np.sign(signal)))[0]
pitch_period = 1 / zero_crossings
print(pitch_period)

A RuntimeWarning: divide by zero encountered in true_divide

B TypeError

C ZeroDivisionError

D No error, prints pitch periods

💡 Hint

Check what happens if zero_crossings contains zero values.

The zero_crossings array contains indices starting at 0, so dividing 1 by zero_crossings causes a divide by zero warning and results in inf values.

Practice

1. What is the main goal of a pitch detection algorithm in signal processing?

easy

A. To find the main frequency or tone in a sound signal

B. To remove noise from a sound signal

C. To increase the volume of a sound signal

D. To convert sound into text

Solution

1. Step 1: Understand pitch detection purpose

   Pitch detection algorithms analyze sound to find the fundamental frequency or main tone.

2. Step 2: Compare options to definition

   Only To find the main frequency or tone in a sound signal describes finding the main frequency, which matches pitch detection's goal.

3. Final Answer:

   To find the main frequency or tone in a sound signal -> Option A

4. Quick Check:

   Pitch detection = main frequency [OK]

Hint: Pitch detection finds the main tone frequency [OK]

Common Mistakes:

• Confusing pitch detection with noise removal
• Thinking pitch detection changes volume
• Mixing pitch detection with speech-to-text

2. Which of the following is the correct Python syntax to compute the autocorrelation of a signal array x using numpy?

easy

A. np.autocorr(x)

B. np.correlate(x, x, mode='full')

C. np.correlation(x, x)

D. np.correlate(x)

Solution

1. Step 1: Recall numpy autocorrelation syntax

   Autocorrelation uses np.correlate with the same array twice and mode='full' for full result.

2. Step 2: Check options for correct function and parameters

   Only np.correlate(x, x, mode='full') uses np.correlate(x, x, mode='full'), which is correct syntax.

3. Final Answer:

   np.correlate(x, x, mode='full') -> Option B

4. Quick Check:

   Autocorrelation = np.correlate(x, x, 'full') [OK]

Hint: Use np.correlate(x, x, mode='full') for autocorrelation [OK]

Common Mistakes:

• Using non-existent function np.autocorr
• Missing second argument in np.correlate
• Wrong function name like np.correlation

3. Given the following Python code snippet for pitch detection using autocorrelation, what is the output of pitch_period?

import numpy as np
x = np.array([0, 1, 0, -1, 0, 1, 0, -1])
correlation = np.correlate(x, x, mode='full')
mid = len(correlation) // 2
pitch_period = np.argmax(correlation[mid+1:]) + 1
print(pitch_period)

medium

A. 2

B. 3

C. 1

D. 4

Solution

1. Step 1: Understand autocorrelation output length and midpoint

   Input length is 8, so correlation length is 15, midpoint at index 7.

2. Step 2: Find max correlation lag after midpoint

   Correlation peaks at lag 4 (pattern repeats every 4 samples), so np.argmax(correlation[8:]) + 1 = 4.

3. Final Answer:

   4 -> Option D

4. Quick Check:

   Pitch period = 4 samples [OK]

Hint: Pitch period = lag with highest autocorrelation after zero lag [OK]

Common Mistakes:

• Choosing zero lag as pitch period
• Off-by-one error in indexing
• Misunderstanding correlation midpoint

4. The following code attempts to find the pitch period but gives incorrect results. What is the main error?

import numpy as np
x = np.array([0, 1, 0, -1, 0, 1, 0, -1])
correlation = np.correlate(x, x, mode='full')
pitch_period = np.argmax(correlation)  # Incorrect line
print(pitch_period)

medium

A. It should use np.min instead of np.argmax

B. It uses the wrong input array for correlation

C. It finds the max correlation over full range including negative lags

D. It misses normalizing the correlation

Solution

1. Step 1: Analyze np.argmax usage on full correlation

   Using np.argmax on full correlation finds max at zero lag (center), not pitch period lag.

2. Step 2: Correct approach is to find max after midpoint

   Pitch period is lag > 0 with max correlation, so search only after midpoint.

3. Final Answer:

   It finds the max correlation over full range including negative lags -> Option C

4. Quick Check:

   Max correlation at zero lag is not pitch period [OK]

Hint: Search max correlation only after zero lag index [OK]

Common Mistakes:

• Taking max correlation at zero lag as pitch
• Ignoring lag indexing after midpoint
• Confusing normalization with lag selection

5. You have a recorded audio signal sampled at 8000 Hz. Using autocorrelation, you find the pitch period is 160 samples. What is the pitch frequency in Hz? How would you calculate it?

hard

A. 50 Hz, calculated as sample_rate / pitch_period

B. 160 Hz, calculated as pitch_period / sample_rate

C. 8000 Hz, the sample rate itself

D. 0.02 Hz, calculated as pitch_period * sample_rate

Solution

1. Step 1: Understand pitch frequency formula

   Pitch frequency = sample rate divided by pitch period (in samples).

2. Step 2: Calculate pitch frequency

   Pitch frequency = 8000 / 160 = 50 Hz.

3. Final Answer:

   50 Hz, calculated as sample_rate / pitch_period -> Option A

4. Quick Check:

   Frequency = 8000 / 160 = 50 Hz [OK]

Hint: Pitch frequency = sample rate ÷ pitch period [OK]

Common Mistakes:

• Dividing pitch period by sample rate instead
• Using sample rate as frequency directly
• Multiplying pitch period by sample rate