5CTA0 · Statistical Signal Processing exam guide

Four blocks. Same skeletons every year.

The written exam is 70% of the grade. It is always the same four exercises — probability, estimation, spectra, detection — with new numbers. This guide teaches the course from zero and trains those skeletons until they are automatic.

Sources: course reader 2023–24, video lectures, official keys 2019–2020, papers 2019–2022, SLT 2024–26.
70%written exam
need ≥ 5.0 here
4exercises, ~3 h
MC + open
1 A4own sheet, both sides
+ calculator

Lab is 30% and there is no opt-out. Pass rule: exam ≥ 5.0 and weighted average ≥ 5.5. This guide is for the written exam.

How to use this

  1. Read a chapter. Do the algebra yourself; do not just look at it.
  2. Close the solution. Do the drill. Then open the spoiler.
  3. When a chapter is dry, sit a past paper under time. Start with the walkthrough on the papers page, then Nov 2022, then the 2022 resit.
  4. Copy the A4 sheet by hand. Typed is allowed; writing it is how it sticks.

Exam language is English, so the guide is English. Notation matches the reader: \(p(x;\theta)\) classical, \(p(x\mid\theta)\) Bayesian, \(r[\tau]\), \(P(e^{j\theta})\).

The four blocks

What the exam actually is

Aid1 A4 both sides (typed or handwritten) + scientific/graphic calculator + dictionary. The 2026–27 guide does not promise a provided formula sheet. Write your own.
ShapeFour exercises, ~3 h. MC + open. After Jan 2019, MC is one correct circle, sprinkled through all four blocks (not a separate Q1). Jan 2019 allowed 1 or 2 correct, with a −0.25 penalty.
PointsTypical split (Nov 2022): 1.5 / 2.75 / 3.0 / 2.75. Spectra is the fattest block. Total 10.
What they gradeFormulation, order, foundation of arguments. A correct number with no likelihood written is not full marks. Shade-the-plot and fill-the-table appear every year.

What actually repeats

Seven papers, 2019–2022. The 2020 resit and the 2022 resit are the same exam. These skeletons come back with new numbers:

Every paperLRT + shade \(P_D / P_{\mathrm{FA}} / P_M\) on a plot. Which region is “decide \(\mathcal H_1\)” is the trap.
5 papersBayes with a complement / base-rate trap. Correlogram in \(\cos(k\theta)\). AR(\(p\)) Yule–Walker + PSD overlay.
4 papersMLE from an iid PDF. CRLB / Fisher / regularity. MAP vs MMSE. MA(\(q\)) from the ACF.
Still liveSpectral factorization (min-phase), ARMA(1,1) → ACF then fake AR(1)/MA(1), Gauss–Newton, matched filter as MC.
Legacy2-tap Wiener as a 2.5-pt design question: only Jan 2019. Keep \(Rw=r\) as the AR predictor; do not drill a numerical Wiener layout.

Methods walked on real questions, then official keys: how to sit the papers.

Álvaro Menéndez Ros · 5CTA0 Q1 2026–27 · built from Canvas material, not from the previous study dump.