6.342 Wavelets, Approximation, and Compression
In charge: Professor Vivek Goyal

Offered Spring 2009 (generally offered alternate Spring semesters)

Study topics including Hilbert space formulation of continuous-time and discrete-time signals, sampling, orthogonal and biorthogonal signal expansions, uncertainty principles and the time-frequency plane, two-channel filter banks, iterated filter banks, discrete wavelet transforms, multiresolution analysis, wavelet bases, regularity, approximation properties, and nonlinear approximation, basics of quantization and source coding compression, denoising, and other image processing using wavelets. Advanced topics from the current research literature.

The course uses the manuscript The World of Fourier and Wavelets by Martin Vetterli, Jelena Kovacevic, and Vivek Goyal.

6.341 Discrete-Time Signal Processing

In charge: Professors Alan Oppenheim and Vivek Goyal

Offered Fall 2008 by Alan Oppenheim (generally offered every Fall semester)

Representation, analysis, and design of discrete time signals and systems. Discrete-time processing of continuous-time signals. Decimation, interpolation, and sampling rate conversion. Flowgraph structures for DT systems. Time- and frequency-domain design techniques for recursive (IIR) and non-recursive (FIR) filters. Linear prediction. Discrete Fourier transform, FFT algorithm. Short-time Fourier analysis and filter banks. Multirate techniques. Hilbert transforms, Cepstral analysis, various applications.