- Introduction to these lecturelets
- Broad overview of EEG data analyses
- How to inspect time-frequency results
- Introduction to Matlab programming
- EEG data and indexing in Matlab
- Overview of time-domain analyses
- Topographical plots
- The three most important equations in neural time series analyses

- Sine waves in time and in frequency
- The dot (a.k.a. inner) product
- The discrete-time Fourier transform
- Complex sine waves and interpreting Fourier coefficients
- Fourier transform frequencies and zero-padding
- Stationarity and effects of violations

- Convolution in the time domain
- Morlet wavelets in time and in frequency
- Convolution via frequency domain multiplication
- Euler's formula and extracting power and phase
- Convolution with many trials
- Effects of Morlet wavelet parameters on results
- Inter-trial phase clustering
- Total vs. phase-locked vs. non-phase-locked power
- Frequency resolution of wavelet convolution

- The Hilbert transform
- Band-pass filtering and the filter-Hilbert method
- Short-time Fourier transform
- Multitaper
- Instantaneous frequency (frequency sliding)

- Power-law scaling and the need for normalization
- Decibel and percent change power normalizations
- Choosing a "baseline"
- Post-analysis temporal downsampling
- Linear vs. logarithmic time-frequency plots
- Accurately recovering data units in FFT and convolution

- Filter, epoch, baseline subtraction, referencing
- Trial rejection
- Independent components analysis for removing artifacts
- Surface Laplacian for cleaning, topoplogical localization, and connectivity

- Intro to connectivity, volume conduction, and time- vs. trial-based connectivity
- Phase-based connectivity analyses
- Power-based connectivity analyses

- Introduction to statistics
- Permutation-based statistics
- Multiple comparisons and their corrections
- Group-level analyses
- Avoiding circular inference

- Vectors and matrices, multiplication, rank
- Least-squares fitting
- Eigendecomposition and PCA
- GED for spatial filtering and dimensionality reduction
- Mathematical discussion of GED