Spectrograms in MATLAB

Introduction

A spectrogram shows how the strength of different sounds or signals changes over time. It helps us see patterns in sounds or signals that change.

To analyze bird songs or animal calls over time.

To check the quality of a recorded speech or music.

To find hidden patterns in machine vibrations for maintenance.

To study heartbeats or brain waves in medical signals.

To detect changes in radio or sonar signals.

Syntax

MATLAB

spectrogram(x,window,noverlap,nfft,fs)

% where:
% x = signal data vector
% window = length or type of window (e.g., hamming)
% noverlap = number of overlapping samples
% nfft = number of FFT points
% fs = sampling frequency

The window helps focus on small parts of the signal.

noverlap controls how much windows overlap to get smoother results.

Examples

Basic spectrogram with 256-sample window, 200 samples overlap, 512 FFT points, and 1000 Hz sampling rate.

MATLAB

spectrogram(x,256,200,512,1000)

Using a Hamming window of length 256, 128 samples overlap, 512 FFT points, and 2000 Hz sampling rate.

MATLAB

spectrogram(x,hamming(256),128,512,2000)

Shorter window of 128 samples, 120 overlap, 256 FFT points, and 8000 Hz sampling rate for higher time resolution.

MATLAB

spectrogram(x,128,120,256,8000)

Sample Program

This code creates a signal with two tones at 100 Hz and 300 Hz. Then it shows the spectrogram to see how these tones appear over time.

MATLAB

% Create a sample signal: two sine waves with different frequencies
fs = 1000; % Sampling frequency 1000 Hz
t = 0:1/fs:2-1/fs; % 2 seconds time vector
x = cos(2*pi*100*t) + cos(2*pi*300*t); % Signal with 100 Hz and 300 Hz components

% Plot spectrogram
figure;
spectrogram(x,256,200,512,fs,'yaxis');
title('Spectrogram of sample signal');
colormap jet;

Important Notes

Choosing window size affects time and frequency detail: smaller windows show time changes better, larger windows show frequency better.

Overlap helps smooth the spectrogram but increases computation time.

Sampling frequency must be set correctly to get accurate frequency axis.

Summary

Spectrograms show how signal frequencies change over time.

Use windows and overlap to balance time and frequency details.

They help find patterns in sounds or signals that change.

Practice

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

easy

A. The total energy of a signal

B. How frequencies change over time in a signal

C. The amplitude of a signal at a single point

D. The phase shift of a signal

Solution

1. Step 1: Understand the purpose of a spectrogram

   A spectrogram is a visual tool that shows how the frequency content of a signal varies over time.

2. Step 2: Compare options with the definition

   Only How frequencies change over time in a signal correctly describes this as frequency changes over time, while others describe different signal properties.

3. Final Answer:

   How frequencies change over time in a signal -> Option B

4. Quick Check:

   Spectrogram = frequency vs time [OK]

Hint: Spectrogram = frequency changes over time [OK]

Common Mistakes:

• Confusing amplitude with frequency
• Thinking spectrogram shows total energy
• Mixing phase shift with frequency content

2. Which of the following is the correct syntax to create a spectrogram in MATLAB for signal x with window size 256 and overlap 128?

easy

A. spectrogram(x,256,128)

B. spectrogram(x,128,256)

C. spectrogram(256,x,128)

D. spectrogram(x,128)

Solution

1. Step 1: Recall MATLAB spectrogram syntax

   The syntax is spectrogram(signal,window,overlap), so the window size comes before overlap.

2. Step 2: Match parameters to syntax

   spectrogram(x,256,128) correctly uses spectrogram(x,256,128) where 256 is window size and 128 is overlap.

3. Final Answer:

   spectrogram(x,256,128) -> Option A

4. Quick Check:

   Correct order: signal, window, overlap [OK]

Hint: Remember: spectrogram(signal, window, overlap) [OK]

Common Mistakes:

• Swapping window and overlap values
• Passing window size as first argument
• Omitting required parameters

3. What will be the output size of the matrix S when running [S,F,T] = spectrogram(x,128,64,256,1000); if x is a 1-second signal sampled at 1000 Hz?

medium

A. 256 rows by 15 columns

B. 128 rows by 16 columns

C. 129 rows by 14 columns

D. 129 rows by 16 columns

Solution

1. Step 1: Calculate frequency bins (rows)

   Frequency bins = nfft/2 + 1 = 256/2 + 1 = 129 rows.

2. Step 2: Calculate time bins (columns)

   Signal length = 1000 samples, window=128, overlap=64, step = 128-64=64 samples.
   Number of segments = floor((1000-128)/64) + 1 = floor(872/64) + 1 = 13 + 1 = 14 columns.

3. Final Answer:

   129 rows by 14 columns -> Option C

4. Quick Check:

   Rows = 129, Columns = 14 [OK]

Hint: Rows = nfft/2+1, columns depend on window and overlap [OK]

Common Mistakes:

• Confusing nfft with window size for rows
• Miscounting number of segments
• Ignoring overlap in time bins calculation

4. Given the code snippet:

x = randn(1,1000);
[S,F,T] = spectrogram(x,256,128,512,1000);
imagesc(T,F,abs(S)); axis xy;

The spectrogram plot looks very blurry. What is the most likely cause?

medium

A. Sampling frequency is too low

B. Overlap is too small, causing gaps in data

C. nfft is smaller than window size, causing error

D. Window size is too large, causing poor time resolution

Solution

1. Step 1: Analyze window size effect on resolution

   A large window size (256) smooths over time, reducing time resolution and causing blur.

2. Step 2: Check other parameters

   Overlap is 128 (50%), which is typical and not causing gaps.
   nfft (512) is larger than window (256), which is valid.
   Sampling frequency (1000) is standard.

3. Final Answer:

   Window size is too large, causing poor time resolution -> Option D

4. Quick Check:

   Large window = poor time resolution [OK]

Hint: Large window = better frequency, worse time resolution [OK]

Common Mistakes:

• Confusing overlap with window size effect
• Assuming nfft smaller than window causes blur
• Blaming sampling frequency for blur

5. You want to analyze a signal with rapidly changing frequencies using MATLAB's spectrogram. Which combination of parameters will best capture quick changes without losing frequency detail?

hard

A. Small window size, large overlap, moderate nfft

B. Large window size, large overlap, small nfft

C. Large window size, small overlap, large nfft

D. Small window size, small overlap, large nfft

Solution

1. Step 1: Understand trade-offs in spectrogram parameters

   Small window size improves time resolution to capture rapid changes.
   Large overlap ensures smooth transitions between windows.
   Moderate nfft balances frequency resolution without excessive computation.

2. Step 2: Evaluate options

   Small window size, large overlap, moderate nfft matches these criteria.
   Small window size, small overlap, large nfft has small overlap, causing gaps.
   Options B and C use large windows, reducing time resolution.

3. Final Answer:

   Small window size, large overlap, moderate nfft -> Option A

4. Quick Check:

   Quick changes need small window + large overlap [OK]

Hint: Small window + large overlap = best for fast changes [OK]

Common Mistakes:

• Using large window for fast changes
• Ignoring overlap size
• Choosing too small nfft losing frequency detail