Signal Processing

Understanding and shaping signals. The mathematics and practice of signal processing: signals and systems, Fourier series and transforms, Laplace and Z transforms, sampling and aliasing, digital FIR/IIR filters, and the DFT/FFT — with runnable Python examples.

• Signals & Systems — The language of signal processing. Learn continuous and discrete signals, classification (periodic, energy/power, even/odd, deterministic/random), basic signals (step, impulse, sinusoid, exponential), system properties (linearity, time-invariance, causality, stability), LTI systems, impulse response and convolution.
• Fourier Series & Transform — Any signal can be built from sinusoids. Learn the Fourier series of periodic signals (square wave harmonics), the Fourier transform and its properties (linearity, time shift, scaling, convolution ↔ multiplication, Parseval), spectra of common signals, bandwidth, and frequency response of LTI systems.
• Laplace Transform — The Laplace transform turns differential equations into algebra. Learn the definition and region of convergence, common transform pairs, properties (derivative, integral, shift), transfer functions, poles and zeros, stability from pole locations, first- and second-order responses (ω_n, ζ, overshoot), and initial/final value theorems.
• Z-Transform — The Z-transform is the Laplace transform for discrete-time systems. Learn the definition and ROC, common pairs, the delay property z⁻¹, difference equations and transfer functions H(z), poles and zeros in the z-plane, stability (|p| < 1), frequency response on the unit circle, and mapping s to z (bilinear transform).
• Sampling & Aliasing — Sampling turns continuous signals into numbers. Learn the Nyquist–Shannon sampling theorem, aliasing and how to calculate alias frequencies, anti-aliasing filters, reconstruction (zero-order hold, sinc interpolation), oversampling and decimation, undersampling (bandpass sampling), and quantisation.
• Digital Filters & DSP — Digital filters process sampled signals in software or hardware. Learn FIR vs IIR, moving-average filters, windowed-sinc FIR design, linear phase and group delay, IIR biquads, filter order estimation, fixed-point implementation, DSP processors and MAC operations — with a Python FIR design.
• DFT & FFT — The discrete Fourier transform computes the spectrum of sampled data, and the FFT computes it fast. Learn the DFT definition, frequency bins and resolution, the radix-2 FFT and its N log N cost, windowing and spectral leakage, zero padding, amplitude scaling, real-signal FFTs, and applications — with a Python spectrum analyser.