## LING525

**Computational Analysis and Modeling of
Biological Signals and Systems**

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.

- (2 weeks) Linear algebra
notation/concepts.

Early Color Vision: psychophysics and physiology of color matching; application of subspace analysis.

[Also: R. Moore, "An Introduction to the Mathematics of Digital Signal Processing", Part I & Part II]

- (1 week) Linear shift-invariant
systems, impulse responses, FIR filters.

- (2 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. Windowing in the time domain; 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. - (1 week) "Introduction to Subspace Methods": Data-dependent coordinate transformations, Applications of eigenvalues, Singular Value Decomposition, PCA, ICA etc. Some non-Fourier approaches to dimensionality-reduction of time-series data.
- (2 weeks) Linear constant-coefficient difference equation form of causal
FIR and IIR filters.

The z transform. More on the z transform and the LPC spectrum. Notes on LPC analysis. Overview of Kalman filtering - (1 week) Sampling. Sample rate conversion; dimensionality and the reconstruction of a signal from subsamples. Sampling of continuous signals: frequency-domain effects of models of sampling.. Effects of quantization.
- (1 week) Recent work in "neural nets": DNNs, RNNs, LSTMs, etc.
- (3 weeks) Other topics. The "kernel trick".

"Cheat Sheet" (for various representations and conversions).

Some readings on time-frequency analysis