The Fourier Transform and Its Applications¶

Course Overview¶

• Institution: Stanford University
• Course code: EE 261
• Track: Signals and Systems
• Tier: S
• Role: Mainline
• Level: Not standardized by provider (use prerequisites)
• Last reviewed: 2026-07-28

Stanford University's The Fourier Transform and Its Applications builds a Fourier-analysis spine from 30 videos, transcripts, nine solved problem sets, and exams, with only small MATLAB utilities showing their age.

Why choose this course

Mainline course. A particularly complete and well-structured option for this track.

Before you start

• Recommended foundation: Engineering Mathematics
• Recommended foundation: Circuit Analysis

Verifiable learning outcomes

• Explain the core models in Signals and Systems, including their assumptions and limits
• Solve representative derivations and problems, checking units, limiting cases, or numerical results
• Complete a reproducible experiment or implementation with raw data, parameters, versions, and verification

Workload and pacing

13 weeks at 9 hours/week. This maintainer planning estimate is derived from course role and the density of public practice and labs; it is not a provider workload promise. Pilot two weeks while logging instruction, practice, lab, and review time, then adjust the remaining plan when actual effort differs by more than 25%.

Safety level

Simulation only. The default practice scope is software, computation, or simulation only; a lab label in the resource inventory does not authorize connecting physical equipment, and any hardware extension requires provider-scope verification and a new risk assessment.

Course Resources¶

Software, hardware, and cost

Software

• Maintainer-suggested open-source/free verification path: Python 3, Jupyter, NumPy, SciPy, and Matplotlib
• The resource inventory lists public code coverage; pin interpreter, dependencies, toolchain, datasets, and PDK versions where applicable

Hardware

• The resource inventory does not list public physical-lab coverage; the maintainer path defaults to computation/simulation. It assumes only a general-purpose computer that can run numerical experiments and retain input/output data; no dedicated physical hardware is assumed. If the provider lists different equipment or compute requirements, follow its course page

Cost note

The suggested software stack is available open source or free; this is maintainer planning, not a provider requirement. If the provider specifies commercial licenses, cloud compute, storage, or institutional resources, costs vary by plan, region, and institution, so no fixed price is asserted here.

Public resource coverage

Resources and access

“Listed by official page” means the link was discovered on a successfully fetched official source on the verification date; it does not guarantee that every region or account can open the target directly. Access does not grant redistribution rights. Re-check the provider page, target link, and third-party notices before downloading, adapting, or publishing material.

Practice and Verification¶

Practice loop

The Fourier Transform and Its Applications · Stanford University EE 261: LTI System Identification and Model-Boundary Audit

This is a maintainer-suggested self-study project for The Fourier Transform and Its Applications · Stanford University EE 261, not an official course assignment. Construct a known LTI system for Signals and Systems, identify it from impulse, frequency, and input-output evidence, and quantify how sampling, truncation, and nonlinearity break the model.

Origin: Maintainer-suggested project

Deliverables

• A specification of system equations, transfer function or state space, and test-signal design
• An executable notebook for generation, identification, convolution or transforms, and plotting
• Raw input-output, impulse-response, frequency-response, and residual data
• A report comparing three model views and analyzing aliasing, leakage, truncation, and nonlinear failure

Verification

• Achieve normalized reconstruction RMSE below 1% on the noiseless baseline
• Document expected and observed behavior at DC, near Nyquist, with finite records, and under amplitude saturation
• Show time-domain convolution and frequency-domain multiplication agree within 1e-8
• Inject a time-varying or nonlinear term and quantify at least threefold residual growth over the LTI baseline

Reproducibility

• Commit model, signal-generation, identification, test, and plotting sources
• Pin sample rate, record length, window, dependencies, and random seeds
• Preserve raw waveforms and intermediate transforms and rebuild the report from raw data with one command

Safety boundary: Simulation only — Use synthetic signals and software models only; any later hardware connection requires a fresh assessment of voltage, grounding, acquisition, and actuator risks.

Risks, gaps, and boundaries

Thirty videos, transcripts, nine solved problem sets, and exams form a strong loop; only the small MATLAB utilities are dated.

Completion evidence

• Weekly learning log with time, questions, corrected errors, decisions, next steps, and links to that week's reproducible artifacts
• Theory dossier with explicit assumptions, notation, derivation, units, and boundary conditions, checked by at least one independent method
• Simulation package with model or netlist, inputs, solver and version, parameter-sweep script, benchmark comparison, expected results, and one rerun command
• Code repository with pinned dependencies and toolchain, a minimal run command, tests or waveform/benchmark checks, expected output, and license notes