Spectrogram generation in SciPy

Introduction

A spectrogram shows how sound or signal frequencies change over time. It helps us see patterns in sounds or signals.

To analyze bird songs or animal sounds to see different notes.

To check machine sounds for unusual noises that mean problems.

To study speech patterns in language learning or speech therapy.

To visualize music notes and beats in a song.

To detect signals in scientific data like earthquakes or heartbeats.

Syntax

SciPy

from scipy.signal import spectrogram
frequencies, times, Sxx = spectrogram(signal, fs, window='hann', nperseg=256, noverlap=None)

signal is your input data, like a list or array of sound values.

fs is the sample rate, how many data points per second.

Examples

Basic spectrogram with default window and segment size.

SciPy

frequencies, times, Sxx = spectrogram(signal, fs=1000)

Using a Hamming window and larger segment size for smoother results.

SciPy

frequencies, times, Sxx = spectrogram(signal, fs=2000, window='hamming', nperseg=512)

Overlap segments by 128 points to get better time resolution.

SciPy

frequencies, times, Sxx = spectrogram(signal, fs=1000, noverlap=128)

Sample Program

This code creates a signal with two tones and shows their frequencies over time using a spectrogram plot.

SciPy

import numpy as np
import matplotlib.pyplot as plt
from scipy.signal import spectrogram

# Create a sample signal: 2 seconds, 1000 Hz sample rate
fs = 1000
T = 2
t = np.linspace(0, T, T*fs, endpoint=False)

# Signal with two frequencies: 50 Hz and 120 Hz
signal = 0.5 * np.sin(2 * np.pi * 50 * t) + 0.3 * np.sin(2 * np.pi * 120 * t)

# Generate spectrogram
frequencies, times, Sxx = spectrogram(signal, fs)

# Plot spectrogram
plt.pcolormesh(times, frequencies, Sxx, shading='gouraud')
plt.ylabel('Frequency [Hz]')
plt.xlabel('Time [sec]')
plt.title('Spectrogram Example')
plt.colorbar(label='Intensity')
plt.show()

Important Notes

The spectrogram output Sxx shows intensity of frequencies over time.

Choosing nperseg affects time and frequency detail: smaller means better time detail, larger means better frequency detail.

Use plt.pcolormesh to visualize the spectrogram nicely.

Summary

Spectrograms help us see how frequencies in a signal change over time.

Use scipy.signal.spectrogram with your signal and sample rate.

Visualize with a color plot to understand frequency intensity.

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