Signals and systems visualizations using scripts

Signals & Systems (8 scripts): Standard signal plots, LTI property testing, animated convolution, Fourier series,reconstruction of signal

Signals & Systems MATLAB Toolkit — Script Descriptions

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All scripts produce MATLAB figure plots. Some include animations.

ss06 requires Symbolic Math Toolbox.

1. ss01_signal_playground.m

Explore standard CT and DT signals. Plots the six textbook signals

side-by-side, computes energy vs power, and demonstrates time shift,

reversal and scaling transformations.

2. ss02_lti_explorer.m

Empirically test system properties. Applies a battery of numerical tests to

four systems for linearity, time-invariance, causality and BIBO stability.

3. ss03_convolution_demo.m

Animated flip-shift-multiply-integrate convolution. Convolves x(t) = rect(t/2)

with h(t) = e^{-t}u(t) and animates each step so students see how the output

y(t) is built up.

4. ss04_fourier_series.m

Reconstruct periodic waveforms from N harmonics. Shows how square, triangle

and sawtooth waves are built harmonic by harmonic and animates the Gibbs

phenomenon.

5. ss05_fourier_transform.m

CT Fourier transform pairs and filtering. Numerically computes magnitude and

phase of common pairs and shows how an ideal low-pass filter kills

high-frequency content.

6. ss06_laplace_solver.m

Solve a 2nd-order ODE symbolically via Laplace transform. Prints Y(s),

partial fractions, and the time-domain solution, then plots it.

(Requires Symbolic Math Toolbox.)

7. ss07_z_transform.m

Pole-zero plot, ROC and difference-equation response. Analyzes

H(z) = (1 + 0.5z^-1) / (1 - 0.9z^-1 + 0.2z^-2).

8. ss08_sampling_aliasing.m

Nyquist rate and aliasing visualiser. Samples a 7 Hz cosine at 8 Hz to show

a 1 Hz alias, then reconstructs a 3 Hz cosine sampled at 20 Hz using ideal

sinc interpolation.