Statistical Signal Processing
Nine weekly decks
Every optimal linear signal processor in this course is one orthogonal projection. The weeks below build the geometry that makes the projection computable, then apply it — as the matched filter, the beamformer, the Wiener filter, the predictor, the adaptive filter and the Kalman filter.
The nine weeks
The course is taught as nine weeks of two lectures, one deck per week, after an opening overview. Each week opens on a question and leaves one idea behind; the notes hold the technical detail.
| Week | Deck | Leaves behind |
|---|---|---|
| 0 | What This Course Is For | A tour: the applications, the one idea, the spiral, a live demo |
| 1 | Why Noise Is Gaussian | Sums of many small independent effects are Gaussian, so two moments suffice |
| 2 | Learning a Constant from Data | An estimator is a random variable, and there is a floor no estimator beats |
| 3 | What an Observation Is Worth | The posterior does the work; the conditional mean is the best estimate |
| 4 | The Shape of a Random Vector | The covariance matrix is a geometry; whitening changes coordinates |
| 5 | Estimation Is Projection | The best linear estimate is a right angle: the normal equations |
| 6 | One Formula, Four Instruments | Matched filter, beamformer, regularized inverse, fusion: one formula |
| 7 | When the Index Is Time | Stationarity, the spectrum, and white noise through a filter |
| 8 | The Wiener Filter | The normal equations become a convolution |
| 9 | Estimation That Keeps Up | Predict, then fuse, recursed: Kalman and the adaptive filters |
Companion material
- Lecture notes — Stochastic Processes and Statistical Signal Processing, the merged book these topics follow.
- Revision guide — the argument of the course in five pages, each result with a line on what it is for and how it connects.