Signals & Systems Mathematics

Describing and transforming signals. Signal classification, standard signals and system properties (linear, time-invariant, causal, stable), impulse response and convolution for LTI systems, and sampling — the mathematical backbone of communications, control and DSP.

• 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.
• Convolution & LTI Systems — Convolution computes the output of any linear time-invariant system from its impulse response. Learn continuous and discrete convolution, the flip-shift-multiply-sum procedure, graphical interpretation, properties (commutative, associative, distributive), step response as integrated impulse response, correlation, and engineering examples — with a Python check against an RC circuit.
• 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.