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.

Practice

1. What does a spectrogram primarily show in signal processing?

easy

A. How signal frequencies change over time

B. The total energy of a signal

C. The raw amplitude values of a signal

D. The phase shift of a signal

Solution

1. Step 1: Understand spectrogram purpose

   A spectrogram is a visual tool that shows frequency content of a signal as it changes over time.

2. Step 2: Compare options to definition

   Only How signal frequencies change over time describes frequency changes over time, which matches the spectrogram's function.

3. Final Answer:

   How signal frequencies change over time -> Option A

4. Quick Check:

   Spectrogram = frequency over time [OK]

Hint: Spectrogram = frequency vs time graph [OK]

Common Mistakes:

• Confusing spectrogram with waveform plot
• Thinking it shows only amplitude
• Mixing phase information with frequency

2. Which Python library is commonly used to create spectrograms?

easy

A. matplotlib

B. pandas

C. scikit-learn

D. numpy

Solution

1. Step 1: Identify libraries for plotting

   matplotlib is widely used for plotting graphs including spectrograms.

2. Step 2: Check other libraries' main uses

   pandas is for data frames, scikit-learn for machine learning, numpy for arrays but not direct plotting.

3. Final Answer:

   matplotlib -> Option A

4. Quick Check:

   Plotting spectrogram = matplotlib [OK]

Hint: Plotting graphs? Think matplotlib [OK]

Common Mistakes:

• Choosing numpy for plotting directly
• Confusing pandas with plotting library
• Selecting scikit-learn which is for ML

3. Given this Python code snippet, what is the shape of the output spectrogram array?

import numpy as np
from scipy.signal import spectrogram

fs = 1280  # Sampling frequency
x = np.sin(2 * np.pi * 50 * np.linspace(0, 1, fs))
f, t, Sxx = spectrogram(x, fs)
print(Sxx.shape)

medium

A. (1000, 1000)

B. (129, 9)

C. (50, 1000)

D. (1000, 129)

Solution

1. Step 1: Understand spectrogram output dimensions

   The spectrogram function returns frequency bins and time bins. For default parameters, frequency bins are nfft/2+1 (default nfft=256), so 129 frequency bins.

2. Step 2: Calculate time bins

   With 1 second signal sampled at 1280 Hz and default windowing, time bins are 9 segments.

3. Final Answer:

   (129, 9) -> Option B

4. Quick Check:

   Frequency bins = 129, Time bins = 9 [OK]

Hint: Spectrogram shape = (freq_bins, time_bins) [OK]

Common Mistakes:

• Assuming output shape matches input length
• Confusing frequency bins with sampling rate
• Mixing up rows and columns in output

4. Identify the error in this code snippet for plotting a spectrogram:

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

fs = 500
x = [1, 2, 3, 4, 5]
f, t, Sxx = spectrogram(x, fs)
plt.specgram(Sxx)
plt.show()

medium

A. Using plt.specgram instead of plt.plot

B. Missing import for numpy

C. Sampling frequency fs is too high

D. Passing Sxx instead of x to plt.specgram

Solution

1. Step 1: Understand spectrogram output and plotting

   The spectrogram function returns frequencies, times, and the spectrogram matrix Sxx. plt.specgram expects raw signal, not Sxx.

2. Step 2: Identify misuse of plt.specgram

   Passing Sxx (already spectrogram data) to plt.specgram causes error; should plot Sxx with plt.imshow or pass raw signal to plt.specgram.

3. Final Answer:

   Passing Sxx instead of x to plt.specgram -> Option D

4. Quick Check:

   Plot raw signal with plt.specgram, not spectrogram matrix [OK]

Hint: plt.specgram needs raw signal, not spectrogram data [OK]

Common Mistakes:

• Passing spectrogram matrix to plt.specgram
• Confusing plt.specgram with plt.imshow
• Ignoring correct input types for plotting

5. You want a spectrogram with smoother frequency resolution but less time detail. Which parameter should you increase?

hard

A. Sampling frequency (fs)

B. Overlap between windows (noverlap)

C. Window size (nperseg)

D. FFT length (nfft) smaller than window size

Solution

1. Step 1: Understand window size effect on spectrogram

   Larger window size increases frequency resolution but reduces time resolution (smoother frequency, less time detail).

2. Step 2: Evaluate other parameters

   Increasing overlap smooths time axis but does not improve frequency resolution as much. Sampling frequency affects max frequency, not resolution. nfft smaller than window size is invalid.

3. Final Answer:

   Window size (nperseg) -> Option C

4. Quick Check:

   Increase window size for better frequency resolution [OK]

Hint: Bigger window = better frequency, worse time detail [OK]

Common Mistakes:

• Increasing overlap to improve frequency resolution
• Changing sampling frequency to affect resolution
• Setting nfft smaller than window size