Prerequisites: Digital signal processing is mainly applied linear algebra. We will also assume some basic knowledge of calculus and probability. The course will review the needed mathematical concepts, but if they are all entirely new to you, you will have to work hard to learn both the basic mathematics and its application. However, a genuine interest in understanding, modeling, or mimicking biological systems will go a long way.

Structure: There will be two class meetings a week -- typically one lecture and one lab demonstration. There will be six exercises using the computer language Matlab.You will do a term project, which can be a summary of existing methods and results in some area of interest to you, or can be new work of your own. Grading will be based on the Matlab exercises (40%), the term project (50%), and class participation (10%).

Syllabus: The details of this syllabus may change, depending on the background and interests of class participants.

1. (1.5 weeks) Linear algebra notation/concepts.
   Applications of eigenvalues, Singular Value Decomposition in subspace-based modeling.
   Early Color Vision: psychophysics and physiology of color matching.
   
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. 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. (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.
5. (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.
6. (2 weeks) 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.
7. (2 weeks) Brain imaging techniques. PET, (f)MRI, MEG. Data analysis techniques for fMRI.
   

[Texts:] There are no required texts for the course. For each topic, we will try to distribute some useful reading materials. You may also find it helpful to refer to the following:

• ``Linear Algebra and Its Applications'', Strang, 1988 (or some other linear algebra text).
• ``Signals and Systems'', Oppenheim et al., 1996.
• ``Discrete-Time Signal Processing'', Oppenheim and Schafer, 1989.
• ``Audition'', Buser and Imbert, 1992.
• ``Foundations of Vision'', Wandell, 1995.
• ``Computer-Based Exercises for Signal Processing using Matlab 5'', McClellan et al., 1998.
• "The Matlab 5 Handbook", Redfern and Campbell, 1998.
• "Mastering Matlab 5", Hanselman and Littlefield, 1998.
• "Computer Explorations in Signals and Systems Using Matlab", Buck et al., 1997.

Since most of these are relatively expensive, and relatively little specific material (if any) will be drawn for the course from each, they are not treated as course texts. However, copies will be made available in the phonetics lab (Williams 623) for your reference.