Part VI — Applied Signal Processing

Booklet: Abridged Math Foundations for Signals and Systems, Lessons 36–44 (PDF).

The DFT in practice — resolution, leakage, windows, the FFT; FIR/IIR filter design and finite word lengths; multirate systems, oversampling, and sigma–delta conversion; random signals and spectrum estimation; Wiener, LMS, and Kalman filtering; detection and digital communication; image processing; audio processing and learned DSP; bench electronics.

27 exercises across Lessons 36–44 — 26 [Hand], 1 [Proof]; three per lesson, and no capstone. Several are drawn from Lyons and the other applied texts, cited by problem number in the booklet.

Exercises

Worked sets are linked below as they are completed.

• Lesson 36 — The DFT in Practice: Resolution, Leakage, Windows, and the FFT — 3 exercises (3 [Hand])
• Lesson 37 — Digital Filters: FIR and IIR Design, and Finite Word Lengths — 3 exercises (3 [Hand])
• Lesson 38 — Multirate Systems, Oversampling, and Sigma–Delta Conversion — 3 exercises (3 [Hand])
• Lesson 39 — Discrete-Time Random Signals and Spectrum Estimation — 3 exercises (2 [Hand], 1 [Proof])
• Lesson 40 — Optimal and Adaptive Filters: Wiener, LMS, and the Kalman Filter — 3 exercises (3 [Hand])
• Lesson 41 — Detection and Digital Communication — 3 exercises (3 [Hand])
• Lesson 42 — Images: Convolution, Filtering, Restoration, Edges, and Motion — 3 exercises (3 [Hand])
• Lesson 43 — Audio Signal Processing: Quantization, Effects, Coding, and Learned DSP — 3 exercises (3 [Hand])
• Lesson 44 — The Electronics Bench: a Working Minimum — 3 exercises (3 [Hand])