Signal Theory — All Chapters
8 chapters covering the full mathematical toolkit of signal processing
Each chapter includes comprehensive theory, worked examples, and interactive Python demonstrations you can run in your browser.
Chapter 1: Signals & Systems
Classification of signals, LTI systems, convolution, deconvolution, Wiener filtering, and regularisation techniques.
Chapter 2: Fourier Series
Trigonometric and complex forms, Dirichlet conditions, Parseval theorem, Gibbs phenomenon, and convergence modes.
Chapter 3: The Fourier Transform
Continuous FT, convolution theorem, Plancherel, uncertainty principle, STFT and spectrograms.
Chapter 4: The Laplace Transform
Region of convergence, transfer functions, poles & zeros, BIBO stability, Bode plots, and partial fractions.
Chapter 5: Sampling & Nyquist
Shannon–Nyquist theorem, aliasing, sinc interpolation, practical ADC/DAC, oversampling, and bandpass sampling.
Chapter 6: DFT & FFT
Discrete Fourier transform, Cooley–Tukey radix-2 FFT, spectral leakage, windowing, zero-padding, and Welch PSD.
Chapter 7: The Z-Transform
Definition, ROC, DTFT relationship, transfer functions, stability via unit circle, inverse Z-transform.
Chapter 8: Digital Filter Design
FIR vs IIR, windowing method, bilinear transform, Butterworth/Chebyshev prototypes, implementation.
Applications Across Sciences
How signal theory connects to quantum mechanics, QFT, astrophysics, medical imaging, seismology, climatology, oceanography, and molecular biology.