Pitch detection algorithm in Signal Processing - Mini Project: Build & Apply

Pitch Detection Algorithm

📖 Scenario: Imagine you are building a simple tool to detect the pitch (frequency) of a musical note from a short audio signal. This is useful in music apps to identify notes played on an instrument.

🎯 Goal: You will create a small program that takes a list of audio sample values, sets a threshold for peak detection, finds the peaks in the signal, and calculates the pitch frequency based on the time between peaks.

📋 What You'll Learn

Create a list of audio samples representing a simple waveform

Set a threshold value to detect peaks in the waveform

Write a loop to find indices of peaks above the threshold

Calculate the pitch frequency from the average distance between peaks

Print the detected pitch frequency

💡 Why This Matters

🌍 Real World

Pitch detection is used in music apps, tuning instruments, and speech analysis to identify the note or tone frequency.

💼 Career

Understanding pitch detection algorithms is useful for audio engineers, music software developers, and data scientists working with sound data.

1

Create the audio sample data

Create a list called audio_samples with these exact values: [0, 1, 3, 7, 4, 2, 0, 1, 4, 8, 4, 3, 1, 0] representing a simple waveform.

Signal Processing

# Create the list audio_samples with the given values
# Your code here

Hint

Use square brackets to create a list and type the numbers exactly as shown.

2

Set the peak detection threshold

Create a variable called threshold and set it to 5 to detect peaks above this value.

Signal Processing

audio_samples = [0, 1, 3, 7, 4, 2, 0, 1, 4, 8, 4, 3, 1, 0]
# Set the threshold variable to 5
# Your code here

Hint

Just assign the number 5 to the variable named threshold.

3

Find peaks above the threshold

Create a list called peak_indices that contains the indices of audio_samples where the value is greater than threshold. Use a for loop with i as the index variable and value as the sample value.

Signal Processing

audio_samples = [0, 1, 3, 7, 4, 2, 0, 1, 4, 8, 4, 3, 1, 0]
threshold = 5
# Create peak_indices list with indices where audio_samples[i] > threshold
# Your code here

Hint

Use enumerate(audio_samples) to get index and value, then check if value > threshold.

4

Calculate and print the pitch frequency

Calculate the average distance between consecutive peaks in peak_indices and store it in avg_distance. Then calculate the pitch frequency as sample_rate / avg_distance where sample_rate is 1000. Finally, print the pitch frequency rounded to 2 decimal places using print(f"Pitch frequency: {pitch:.2f} Hz").

Signal Processing

audio_samples = [0, 1, 3, 7, 4, 2, 0, 1, 4, 8, 4, 3, 1, 0]
threshold = 5
peak_indices = []
for i, value in enumerate(audio_samples):
    if value > threshold:
        peak_indices.append(i)
# Calculate avg_distance and pitch frequency, then print the pitch
# Your code here

Hint

Calculate intervals between peaks, average them, then divide sample_rate by average distance.

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