signal-processing
4 free lessons tagged signal-processing across Math. Each one is a short sequence of focused steps with narration and a five-question quiz at the end — take them in any order, no signup required.
Reading a Spectrum Without Fooling Yourself
A spectrum shows you artefacts of the analysis alongside the signal, and telling them apart is a learnable skill. This lesson covers spectral leakage, what windows buy and what they cost, why zero-padding does not add resolution, and the hard trade a spectrogram forces between knowing when and knowing what.
Convolution and Filters: Shaping a Signal
A filter is fully described by what it does to a single impulse, and applying it is a convolution. This lesson builds that idea, shows why the frequency domain turns convolution into plain multiplication, and works through the trade-offs that make real filters ring, lag, or cost more than they need to.
Sampling and Aliasing: The Rule You Cannot Break
Turning a continuous signal into numbers is safe only above a specific rate, and below it the damage is silent and permanent. This lesson derives the Nyquist limit, shows exactly where a too-high frequency reappears, and explains why the fix has to be analogue and has to happen before the converter.
The Frequency Domain: Why Everything Is Sinusoids
The same signal can be written as a function of time or as a recipe of frequencies. This lesson explains why sinusoids in particular get that job, builds the discrete Fourier transform, and shows how the FFT turned a quadratic computation into one you can run on a million samples in a fraction of a second.