Spectrogram generation in SciPy - Mini Project: Build & Apply

Spectrogram Generation with SciPy

📖 Scenario: Imagine you are analyzing sound recordings to understand their frequency content over time. A spectrogram is a useful tool that shows how the frequencies in a sound change as time passes.In this project, you will use Python's scipy library to generate a spectrogram from a simple sound signal.

🎯 Goal: You will create a simple sound signal, configure parameters for the spectrogram, generate the spectrogram using SciPy, and finally display the spectrogram data.

📋 What You'll Learn

Create a numpy array representing a sound signal

Set a sampling frequency variable

Use SciPy's spectrogram function to compute the spectrogram

Print the shape of the spectrogram data

💡 Why This Matters

🌍 Real World

Spectrograms are widely used in audio processing, speech analysis, and music technology to study how sound frequencies vary over time.

💼 Career

Understanding spectrogram generation is useful for roles in audio engineering, data analysis, and machine learning involving time-series or audio data.

1

Create a simple sound signal

Import numpy as np. Create a variable called fs and set it to 1000 to represent the sampling frequency in Hertz. Create a time array called t using np.linspace from 0 to 1 second with fs points. Create a signal called signal as a sine wave with frequency 5 Hz using np.sin(2 * np.pi * 5 * t).

SciPy

# Import numpy as np
# Create fs = 1000
# Create t using np.linspace from 0 to 1 with fs points
# Create signal as sine wave with frequency 5 Hz

Hint

Use np.linspace to create the time array and np.sin to create the sine wave.

2

Import spectrogram function and set parameters

Import spectrogram from scipy.signal. Create a variable called nperseg and set it to 100 to define the length of each segment for the spectrogram.

SciPy

import numpy as np
fs = 1000
t = np.linspace(0, 1, fs, endpoint=False)
signal = np.sin(2 * np.pi * 5 * t)
# Import spectrogram from scipy.signal
# Set nperseg = 100

Hint

Use from scipy.signal import spectrogram to import the function.

3

Generate the spectrogram

Use the spectrogram function with arguments signal, fs, and nperseg. Assign the returned values to variables frequencies, times, and Sxx.

SciPy

import numpy as np
fs = 1000
t = np.linspace(0, 1, fs, endpoint=False)
signal = np.sin(2 * np.pi * 5 * t)
from scipy.signal import spectrogram
nperseg = 100
# Generate spectrogram and assign to frequencies, times, Sxx

Hint

Call spectrogram(signal, fs, nperseg=nperseg) and unpack the result.

4

Display the spectrogram shape

Print the shape of the spectrogram data array Sxx using print(Sxx.shape).

SciPy

import numpy as np
fs = 1000
t = np.linspace(0, 1, fs, endpoint=False)
signal = np.sin(2 * np.pi * 5 * t)
from scipy.signal import spectrogram
nperseg = 100
frequencies, times, Sxx = spectrogram(signal, fs, nperseg=nperseg)
# Print the shape of Sxx

Hint

Use print(Sxx.shape) to see the size of the spectrogram matrix.

Practice

1. What does the scipy.signal.spectrogram function primarily compute from a signal?

easy

A. The frequency content of the signal over time

B. The total energy of the signal

C. The average amplitude of the signal

D. The phase shift of the signal

Solution

1. Step 1: Understand the purpose of spectrogram

   A spectrogram shows how frequencies in a signal change over time, so it computes frequency content over time.

2. Step 2: Compare with other options

   Total energy, average amplitude, and phase shift are different signal properties, not what spectrogram calculates.

3. Final Answer:

   The frequency content of the signal over time -> Option A

4. Quick Check:

   Spectrogram = frequency over time [OK]

Hint: Spectrogram = frequency changes over time [OK]

Common Mistakes:

• Confusing spectrogram with total energy calculation
• Thinking it returns average amplitude only
• Assuming it gives phase information

2. Which of the following is the correct way to import the spectrogram function from scipy?

easy

A. from scipy import spectrogram

B. import scipy.spectrogram

C. from scipy.signal import spectrogram

D. import spectrogram from scipy.signal

Solution

1. Step 1: Recall correct import syntax for functions

   Functions inside submodules are imported using 'from module.submodule import function'.

2. Step 2: Check each option

   from scipy.signal import spectrogram matches this syntax exactly. Options B, C, and D are invalid Python import statements.

3. Final Answer:

   from scipy.signal import spectrogram -> Option C

4. Quick Check:

   Correct import syntax = from scipy.signal import spectrogram [OK]

Hint: Use 'from scipy.signal import spectrogram' [OK]

Common Mistakes:

• Using 'import scipy.spectrogram' which is invalid
• Trying 'from scipy import spectrogram' ignoring submodule
• Incorrect import order like 'import spectrogram from ...'

3. What will be the shape of the frequency array returned by f, t, Sxx = spectrogram(signal, fs=1000, nperseg=256) if signal length is 1024?

medium

A. (256,)

B. (129,)

C. (512,)

D. (1024,)

Solution

1. Step 1: Understand frequency bins from nperseg

   The frequency array length is nperseg/2 + 1 due to FFT symmetry, so 256/2 + 1 = 129.

2. Step 2: Confirm other options

   256 is the segment length, not frequency bins. 512 and 1024 are unrelated to frequency array size here.

3. Final Answer:

   (129,) -> Option B

4. Quick Check:

   Frequency bins = nperseg/2 + 1 = 129 [OK]

Hint: Frequency bins = nperseg/2 + 1 [OK]

Common Mistakes:

• Assuming frequency array length equals nperseg
• Confusing signal length with frequency bins
• Ignoring FFT symmetry in frequency output

4. Given this code snippet, what is the error?

from scipy.signal import spectrogram
signal = [1, 2, 3, 4, 5]
fs = 100
f, t, Sxx = spectrogram(signal, nperseg=256, fs=fs)

medium

A. nperseg is larger than signal length causing a warning or error

B. fs parameter is missing

C. spectrogram function is not imported correctly

D. signal must be a numpy array, not a list

Solution

1. Step 1: Check parameters and signal length

   Signal length is 5, but nperseg is 256, which is larger than signal length.

2. Step 2: Understand spectrogram behavior

   When nperseg > signal length, scipy issues a warning or error because segment size can't exceed signal length.

3. Final Answer:

   nperseg is larger than signal length causing a warning or error -> Option A

4. Quick Check:

   nperseg > signal length causes error [OK]

Hint: nperseg must be ≤ signal length [OK]

Common Mistakes:

• Ignoring nperseg size relative to signal length
• Thinking fs is missing when it is provided
• Assuming list input causes error (it works but numpy array preferred)

5. You want to generate a spectrogram for a noisy signal sampled at 2000 Hz. To improve time resolution, which parameter should you decrease in scipy.signal.spectrogram?

hard

A. window

B. fs

C. noverlap

D. nperseg

Solution

1. Step 1: Understand time vs frequency resolution trade-off

   Decreasing nperseg (segment length) improves time resolution but reduces frequency resolution.

2. Step 2: Check other parameters

   fs is sample rate, noverlap controls overlap, window shapes segments but doesn't directly improve time resolution.

3. Final Answer:

   nperseg -> Option D

4. Quick Check:

   Decrease nperseg for better time resolution [OK]

Hint: Lower nperseg for better time resolution [OK]

Common Mistakes:

• Trying to change fs which is fixed sample rate
• Confusing noverlap with time resolution
• Changing window type expecting time resolution change