MATLAB - Plot Spectrogram

Visualizing Signals with Spectrograms in MATLAB

A spectrogram is a powerful tool for visualizing the frequency content of a signal as it changes over time. It’s essential in fields like audio processing, communications, and vibration analysis. MATLAB’s Signal Processing Toolbox™ provides the spectrogram function to easily compute and display these insightful plots.

What is a Spectrogram?

A spectrogram is a 3D plot displayed as a 2D image. It shows:

• Time on the x-axis.
• Frequency on the y-axis.
• Signal Power/Magnitude as the color intensity at each time-frequency point.

It’s generated by computing the Short-Time Fourier Transform (STFT), which involves breaking the signal into small, overlapping time windows and calculating the Fourier transform for each window.

The spectrogram Function

The primary syntax for generating and plotting a spectrogram is:

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

Let’s break down the key parameters:

• x: Your input signal vector.
• window: A vector defining the windowing function (e.g., hamming(256)). This shapes the signal segments to reduce spectral leakage. The window length determines the trade-off between time and frequency resolution.
• noverlap: The number of samples that overlap between consecutive windows. A typical value is 50% of the window length, which ensures smooth transitions.
• nfft: The number of points for the Fast Fourier Transform (FFT). A larger nfft provides finer frequency resolution.
• fs: The sampling frequency of the signal. This is crucial for correctly labeling the frequency axis in Hertz.
• 'yaxis': An optional argument that plots the spectrogram directly with time on the x-axis and frequency on the y-axis.

Key Concept: The Time-Frequency Trade-off

• A short window provides good time resolution (you can pinpoint when a frequency event occurs) but poor frequency resolution (it’s hard to distinguish between two close frequencies).
• A long window provides good frequency resolution but poor time resolution.

Practical Examples

Example 1: A Chirp Signal

A chirp signal is perfect for demonstrating a spectrogram because its frequency changes over time. Let’s create a signal that sweeps from 100 Hz to 400 Hz.

% --- Signal Parameters ---
samplingFreq = 1000; % Hz
duration = 2; % seconds
timeVector = 0:1/samplingFreq:duration-1/samplingFreq;

% --- Create a linear chirp signal ---
initialFreq = 100; % Hz
finalFreq = 400; % Hz
chirpSignal = chirp(timeVector, initialFreq, duration, finalFreq, 'linear');

% --- Spectrogram Parameters ---
windowLength = 256; % samples
overlap = round(0.5 * windowLength); % 50% overlap
nfft = 512; % FFT points

% --- Generate and Plot Spectrogram ---
figure;
spectrogram(chirpSignal, hamming(windowLength), overlap, nfft, samplingFreq, 'yaxis');
title('Spectrogram of a Linear Chirp Signal');

% Add a colorbar to show power levels
colorbar;

The resulting plot will clearly show a diagonal line, starting at 100 Hz at t=0 and rising to 400 Hz at t=2, visually confirming the signal’s changing frequency content.

Example 2: Analyzing a Sum of Sines

Now, let’s analyze a signal composed of two distinct sine waves, one of which appears only for a short duration.

samplingFreq = 1000; % Hz
timeVector = 0:1/samplingFreq:2-1/samplingFreq;

% A 50 Hz sine wave present for the whole duration
sine1 = sin(2 * pi * 50 * timeVector);

% A 200 Hz sine wave present only from t=0.5s to t=1.5s
sine2 = sin(2 * pi * 200 * timeVector);
sine2(timeVector < 0.5 | timeVector > 1.5) = 0; % Gating the signal

combinedSignal = sine1 + sine2;

% --- Generate and Plot Spectrogram ---
figure;
spectrogram(combinedSignal, 128, 120, 128, samplingFreq, 'yaxis');
title('Spectrogram of a Gated Sinusoid');
colorbar;

The spectrogram for this example will show two horizontal lines. One line will be at 50 Hz, spanning the entire 2-second duration. The second, brighter line will appear at 200 Hz, but only between the 0.5 and 1.5-second marks, demonstrating the spectrogram’s ability to localize signals in both time and frequency.

Common Errors & Practical Tips

• Error: Undefined function 'spectrogram': This means the Signal Processing Toolbox™ is not installed or not active. You can install it from the Add-Ons menu.
• Plot looks ‘smeared’ or ‘blocky’: Your time-frequency resolution is not well-matched to your signal. Experiment with the windowLength. A shorter window improves time resolution (less smearing); a longer window improves frequency resolution (less blockiness in frequency).
• Frequency axis is incorrect: You likely forgot to provide the correct sampling frequency fs as an argument to the spectrogram function. Without it, the y-axis will be in normalized frequency.
• Interactive Analysis: For interactive exploration, use pspectrum(signal, fs, 'spectrogram'). This creates a plot where you can zoom, pan, and measure peaks without regenerating the spectrogram.