Spectrogram visualization in Signal Processing

Introduction

A spectrogram shows how sound or signal frequencies change over time. It helps us see patterns we can't hear or see directly.

To analyze bird songs or animal sounds to understand their patterns.

To check the quality of a recorded voice or music by seeing frequency changes.

To find hidden signals or noises in machine vibrations for maintenance.

To study speech patterns in language learning or speech therapy.

To visualize heartbeats or brain waves in medical tests.

Syntax

Signal Processing

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

frequencies, times, Sxx = spectrogram(signal, fs)
plt.pcolormesh(times, frequencies, 10 * np.log10(Sxx))
plt.ylabel('Frequency [Hz]')
plt.xlabel('Time [sec]')
plt.title('Spectrogram')
plt.colorbar(label='Intensity [dB]')
plt.show()

signal is your input data, like sound or vibration.

fs is the sampling rate, how many samples per second.

Examples

Basic spectrogram with a 1000 Hz sampling rate.

Signal Processing

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

Specifies segment length to get better frequency resolution.

Signal Processing

frequencies, times, Sxx = spectrogram(signal, fs=2000, nperseg=256)

Uses smooth shading for nicer visualization.

Signal Processing

plt.pcolormesh(times, frequencies, 10 * np.log10(Sxx), shading='gouraud')

Sample Program

This code creates a signal that changes frequency after 1 second. The spectrogram shows this change clearly.

Signal Processing

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 changing over time
signal = np.sin(2 * np.pi * 50 * t) * (t < 1) + np.sin(2 * np.pi * 120 * t) * (t >= 1)

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

# Plot spectrogram
plt.figure(figsize=(8, 4))
plt.pcolormesh(times, frequencies, 10 * np.log10(Sxx), shading='gouraud')
plt.ylabel('Frequency [Hz]')
plt.xlabel('Time [sec]')
plt.title('Spectrogram visualization of changing frequencies')
plt.colorbar(label='Intensity [dB]')
plt.tight_layout()
plt.show()

Important Notes

Use 10 * np.log10(Sxx) to convert power to decibels for better visualization.

Adjust nperseg to balance time and frequency detail.

Shading='gouraud' makes the image smoother and easier to read.

Summary

Spectrograms show how frequencies in a signal change over time.

They help find patterns in sounds or vibrations you can't hear directly.

Use libraries like scipy.signal and matplotlib to create and display spectrograms easily.