Part V — The Signals-and-Systems Core

Booklet: Abridged Math Foundations for Signal Processing, Machine Learning, and Artificial Intelligence, Lessons 24–30 (PDF).

Signals and system properties; LTI systems and convolution; Fourier series; the continuous- and discrete-time Fourier transforms; frequency response and filtering; sampling and aliasing, and exact finite sampling of band-limited periodic signals by the DFT; Laplace and \(z\)-transforms.

28 exercises across Lessons 24–30 — 14 [Hand], 14 [Proof].

Exercises

Worked sets are linked below as they are completed.

• Lesson 24 — Signals and Systems — 4 exercises (2 [Hand], 2 [Proof])
• Lesson 25 — LTI Systems and Convolution — 4 exercises (2 [Hand], 2 [Proof])
• Lesson 26 — Fourier Series — 4 exercises (2 [Hand], 2 [Proof])
• Lesson 27 — The Continuous-Time Fourier Transform — 4 exercises (2 [Hand], 2 [Proof])
• Lesson 28 — The Discrete-Time Fourier Transform and Frequency Response — 4 exercises (2 [Hand], 2 [Proof])
• Lesson 29 — Sampling — 4 exercises (2 [Hand], 2 [Proof])
• Lesson 30 — Laplace and \(z\)-Transforms, a Working Minimum — 4 exercises (2 [Hand], 2 [Proof])