# MATLAB Reference Index

This index routes an AI coworker to relevant parts of the four source-note
PDFs without loading the entire 628-page library. The PDFs are available
through `SOURCE_LINKS.md` and are not bundled with this project. Page numbers
below are PDF page numbers. Figures are often part of the explanation and
should be inspected when a topic is selected.

## Quick Routing

| Need | Start here |
| --- | --- |
| MATLAB syntax, plotting, functions, statistics, fitting | `MasterMATLABGuidedProblems_CourseNotes.pdf` |
| FFT theory, scaling, phase, stationarity, STFT | `MasterTheFourierTransformMATLABPython.pdf` |
| Denoising, filtering, convolution, wavelets, features | `SignalProcessingProblemsMATLABPython.pdf` |
| Vectors, matrices, rank, systems, inverse, projections | `Incomplete linear algebra3.pdf` |

## Topic Index

### Array and Matrix Programming

- General vectors and matrices: Guided Problems, Section 3, p. 9
- Command statements and looping: Guided Problems, Section 4, p. 11
- Functions and input checking: Guided Problems, Section 13, pp. 113-117
- Find, minimum, maximum, and logical selection: Guided Problems,
  Section 14, pp. 118-124
- Matrix analysis: Guided Problems, Section 20, pp. 183-210
- Vectorizing MATLAB code: Signal Processing, pp. 123-124
- Broadcasting and matrix arithmetic: Linear Algebra, p. 52
- Standard, Hadamard, and layered matrix multiplication: Linear Algebra,
  pp. 53-84

### Plotting and Visualization

- 2D plotting: Guided Problems, Section 8, pp. 35-67
- 3D plotting: Guided Problems, Section 9, pp. 68-84
- Data animation: Guided Problems, Section 11, pp. 97-103
- Interactive sigmoid parameter visualization: Guided Problems,
  pp. 104-113
- Matrix and transform visualizations: Guided Problems, Section 20,
  pp. 183-210

### Functions, Models, and Fitting

- Functions and anonymous functions: Guided Problems, pp. 113-117
- Calculus and differential equations: Guided Problems, pp. 125-132
- Nonlinear model fitting: Guided Problems, pp. 240-248
- Fit a three-parameter sine wave with `fminsearch`: Guided Problems, p. 245
- Gaussian, piecewise-linear, circle, and oval fitting: Guided Problems,
  pp. 240-248

### Fourier Transform Foundations

- Conceptual Fourier applications: Fourier Notes, pp. 2-15
- Foundations and complex sinusoids: Fourier Notes, pp. 16-30
- Discrete Fourier transform: Fourier Notes, pp. 31-45
- Accurate Fourier coefficient scaling: Fourier Notes, pp. 38-39
- Phase interpretation: Fourier Notes, pp. 39-40
- Inverse transform and band-stop filtering: Fourier Notes, pp. 46-48
- FFT and inverse FFT: Fourier Notes, pp. 49-55
- Fourier transform as matrix multiplication: Linear Algebra, p. 76

### Sampling, Resolution, and Stationarity

- Frequency resolution and zero padding: Fourier Notes, pp. 56-63
- Aliasing, stationarity, and violations: Fourier Notes, pp. 64-81
- Windowing and Welch's method: Fourier Notes, p. 80
- FFT versus Welch power estimates: Guided Problems, pp. 170-173
- FFT length and frequency resolution notes: Signal Processing, p. 117

### Time-Frequency Analysis

- Manual short-time Fourier transform construction: Fourier Notes,
  pp. 76-79
- STFT of a chirp: Fourier Notes, p. 79
- Spectrogram of a bird call: Guided Problems, pp. 174-175
- Spectrogram of birdsong: Signal Processing, p. 34
- Time-frequency analysis with complex Morlet wavelets:
  Signal Processing, pp. 73-81
- Manual wavelet-convolution time-frequency analysis:
  Guided Problems, pp. 181-183

### Filtering and Convolution

- Time-domain and frequency-domain filtering: Guided Problems,
  pp. 155-168
- FIR, IIR, Butterworth, low-pass, high-pass, and narrow-band filters:
  Signal Processing, pp. 40-59
- Causal versus zero-phase filtering: Signal Processing, p. 45
- Edge effects and reflection: Signal Processing, pp. 45-47
- Time-domain convolution and the convolution theorem:
  Signal Processing, pp. 59-65
- Gaussian and tapered convolution filters: Signal Processing, pp. 66-73
- Fourier-domain convolution and filtering applications:
  Fourier Notes, pp. 88-97

### Cleaning, Resampling, and Features

- Univariate time-series cleaning: Guided Problems, pp. 133-143
- Multivariate time-series cleaning: Guided Problems, pp. 144-154
- Mean, Gaussian, median, and polynomial denoising:
  Signal Processing, pp. 8-27
- Resampling, interpolation, extrapolation, and dynamic time warping:
  Signal Processing, pp. 82-90
- Outlier detection: Signal Processing, pp. 90-96
- Feature detection, FWHM, area, and EMG movement:
  Signal Processing, pp. 96-106
- Variance, RMS, SNR, coefficient of variation, and entropy:
  Signal Processing, pp. 106-116

### Linear Algebra

- Vectors, dot products, geometry, complex vectors, and span:
  Linear Algebra, pp. 12-42
- Matrices, transpose, trace, and broadcasting: Linear Algebra, pp. 43-52
- Matrix multiplication, transformations, norms, and symmetry:
  Linear Algebra, pp. 53-84
- Matrix rank: Linear Algebra, pp. 85-94
- Column, row, null, and left-null spaces: Linear Algebra, pp. 95-102
- Systems of equations, elimination, and RREF: Linear Algebra, pp. 103-114
- Determinants: Linear Algebra, pp. 115-121
- Inverse, pseudoinverse, and why to avoid explicit inversion:
  Linear Algebra, pp. 122-143
- Projections and orthogonalization: Linear Algebra, pp. 144-145
- SVD, PCA, QR, covariance, and eigenvector examples:
  Guided Problems, pp. 183-210

## Source Documents

### `MasterMATLABGuidedProblems_CourseNotes.pdf`

- 253 pages
- Broadest reference
- MATLAB R2020-era notes
- Particularly useful for problem formulation, visualization, functions,
  time-series work, matrix analysis, statistics, and fitting

### `MasterTheFourierTransformMATLABPython.pdf`

- 104 pages
- MATLAB and Python
- Particularly useful for conceptual Fourier explanations, coefficient
  scaling, phase, resolution, stationarity, STFT, and image transforms

### `SignalProcessingProblemsMATLABPython.pdf`

- 126 pages
- MATLAB and Python
- Particularly useful for practical denoising, filtering, convolution,
  wavelets, resampling, outliers, and feature extraction

### `Incomplete linear algebra3.pdf`

- 145 pages
- Incomplete course record, but substantial through matrix inverse and the
  start of projections
- Particularly useful for geometric explanations, matrix operations, rank,
  matrix spaces, solving systems, and numerical caution around inverses

## Retrieval Rules

1. Start with this index and `MATLAB_SIGNATURE_METHODS.md`.
2. Read the smallest relevant page range.
3. Inspect the figures when they communicate the method.
4. Treat the notes as a source of insight and prior practice, not as current
   API documentation.
5. Verify current MATLAB syntax and release-sensitive behavior separately.
