How to Use stem() Function in MATLAB to Plot Discrete-Time Signals
The stem() function in MATLAB is built specifically for visualizing discrete-time signals and sequences. While plot() connects data points with continuous lines, doing so on sampled or digital data is mathematically misleading. stem() fixes this by drawing a vertical line from the baseline to each data point topped with a marker—matching how discrete signals appear in DSP textbooks and engineering papers.
plot() for continuous functions and smooth physical signals.stem() for discrete-time, digital, or sampled data.h = stem(Y)
% Plots Y values against their index numbers h = stem(X, Y)
% Plots Y values at custom X coordinates h = stem(..., 'filled') % Fills the top markers h = stem(ax, ...) % Targets a specific axes object h = stem(..., Name, Value)% Customizes colors, line widths, and marker types% Define a sequence x[n] from n = 0 to 10 n = 0:10;
x = [0 1 2 3 2 1 0 -1 -2 -1 0];
stem(n, x, 'filled', 'MarkerFaceColor', 'r', 'LineWidth', 1.5);
title('Basic Discrete Sequence x[n]');
xlabel('Sample index n');
ylabel('Amplitude');
grid on;n = -5:10;
delta = (n == 0);
% Kronecker delta δ[n] step = (n >= 0);
% Unit step u[n] sub
plot(2,1,1);
stem(n, delta, 'filled', 'MarkerSize', 8);
title('Unit Impulse δ[n]');
grid on;
sub
plot(2,1,2);
stem(n, step, 'filled', 'Color', 'm');
title('Unit Step u[n]');
grid on;[X, Y] = meshgrid(-5:1:5, -5:1:5);
Z = X .* exp(-X.^2 - Y.^2);
% 3D Gaussian surface points stem3(X, Y, Z, 'filled', 'MarkerSize', 6);
title('3D Discrete Surface using stem3()');
xlabel('X');
ylabel('Y');
zlabel('Z');
colorbar;b = [1 0.5];
a = [1 -0.9];
% IIR filter coefficients [h, n] = impz(b, a, 30);
% Calculate impulse response stem(n, h, 'filled', 'MarkerFaceColor', 'g');
title('Impulse Response of H(z) = (1 + 0.5z^{-1}) / (1 - 0.9z^{-1})');
xlabel('n');
ylabel('h[n]');
grid on;| Feature | stem() | plot() |
|---|---|---|
| Discrete Data Representation | Accurate and clear | Misleading (implies continuous values between points) |
| Signal Processing Standard | Yes (DSP & digital filters) | No |
| Visual Marker & Vertical Line | Yes | No |
| Baseline Control | Yes (via BaseLine property) | No |
Whenever you are working with sequences, digital filter responses, DFT/FFT outputs, or discrete sampled data, use stem() to keep your plots mathematically accurate.
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