Signal Processing, Communications, and Information Theory¶

Audience¶

Learners moving from Fourier analysis to digital communications, wireless systems, and coding

Final outcome¶

Implement a reproducible link with synchronization, modulation/demodulation, channel coding, and measured error rates.

Stages¶

Signals and probability¶

Selection rule: Complete all 4 required courses; use the other 1 option only to close a specific gap.

• Linear Algebra — Required; MIT; Mainline; S
• Probabilistic Systems Analysis and Applied Probability — Required; MIT; Mainline; S
• Signals and Systems — Required; MIT; Mainline; S
• The Fourier Transform and Its Applications — Required; Stanford University; Mainline; S
• Introduction to Communication, Control, and Signal Processing — Optional supplement; MIT; Supplement; B

Stage exit criterion: Analytically derive and numerically verify the time-domain, frequency-domain, and stochastic responses of one LTI system in a single notebook; Parseval energy residual must be below 1%, and the Monte Carlo mean must fall within the analytical 95% confidence interval.

DSP implementation¶

Selection rule: Complete all 1 required course and choose 1 of 5 elective options.

• Digital Signal Processing — Required; MIT; Mainline; S
• Discrete-Time Signal Processing — Elective option; MIT; Alternative; A
• Digital Signal Processing 1: Basic Concepts and Algorithms — Elective option; EPFL; Alternative; A
• Digital Signal Processing 2: Filtering — Elective option; EPFL; Alternative; A
• Digital Signal Processing 3: Analog versus Digital — Elective option; EPFL; Alternative; A
• Digital Signal Processing 4: Applications — Elective option; EPFL; Alternative; A

Stage exit criterion: Implement a filtering or spectral-processing pipeline and verify passband, stopband, and aliasing requirements with synthetic and real samples; also report reproducible floating-point versus fixed-point SNR, runtime, and memory comparisons.

Communications and coding¶

Selection rule: Complete all 2 required courses and choose 1 of 2 elective options. The other course is an optional supplement and does not count toward the elective requirement.

• Introduction to EECS II: Digital Communication Systems — Required; MIT; Mainline; S
• Principles of Digital Communications I — Elective option; MIT; Mainline; S
• Principles of Digital Communication II — Optional supplement; MIT; Mainline; S
• Information Theory — Required; Stanford University; Mainline; A
• Wireless Communications — Elective option; Stanford University; Alternative; A

Stage exit criterion: Build an end-to-end link with synchronization, modulation, channel, and error correction, using fixed seeds to plot BER at at least six Eb/N0 points; include a theory or baseline comparison, confidence intervals, and synchronization-failure rate.

Execution rules¶

• Follow each stage's selection rule: complete every required course and the stated number of electives; when complete path options are provided, choose one and finish every course in its listed order; use optional supplements only to close a specific gap.
• Produce at least one reproducible artifact per stage and include failed attempts in the retrospective.
• Work involving mains voltage, high voltage, RF exposure, lasers, chemicals, or fabrication equipment requires local-law compliance and qualified supervision.