This syllabus will change to reflect the background and interests of class participants. We'll start with an adaptation of the syllabus that was used the last time the course was given, and work from there. Some new lecture notes will be provided, and the links below (which start as previous years' versions) will be updated and expanded.

1. (2 weeks) Linear algebra notation/concepts.
   Early Color Vision: psychophysics and physiology of color matching; application of subspace analysis.
   
2. (1.5 weeks) Linear shift-invariant systems, impulse responses, FIR filters.
   
3. (3 weeks) Frequency-domain representations. Euler's formula; background of the DFT; properties of the DFT;the Fourier family. The DFT as a rotation of coordinates. Frequency and amplitude modulation, resonances. Windowed frequency measures: spectrograms.
   Frequency-domain analysis in biological systems: tonotopic mapping in the auditory system. Frequency-domain processing of sound and images. Spectral shaping, pitch detection. Analyzing natural vocalizations.
4. (1 week) Data-dependent coordinate transformations: Applications of eigenvalues, Singular Value Decomposition, PCA, ICA etc. in subspace-based modeling.
5. (2 weeks) Linear constant-coefficient difference equation form of causal FIR and IIR filters. The z transform.. State and boundary conditions, stability and causality. LP analysis. Relationship to ideal acoustic tube; reflection coefficient form of recursive filter.
6. (1 week) Sampling. Sample rate conversion through the example of wavetable oscillators. Dimensionality and the reconstruction of a signal from subsamples. Sampling of continuous signals: frequency-domain effects of models of sampling.. Effects of quantization. Invariance to translation, dilation and rotation. Representing continuous signals with finite cell populations.
7. (3 weeks) Other topics, such as: Analysis of amplitude- and frequency-modulated sinusoids. In past years, we've looked at: Multi-rate and multi-scale processing. Scale-space, pyramids, wavelets, steerable filters. Biological representations of sound and light. Multi-scale, multi-orientation image analysis. Perceptual distortion measures. Brain imaging techniques. PET, (f)MRI, MEG. Data analysis techniques for fMRI.