ACM 126 ab - Wavelets and Modern Signal Processing

Institution:

California Institute of Technology

Subject:

Applied and Computational Mathematics

Description:

The aim is to cover the interactions existing between applied mathematics, namely applied and computational harmonic analysis, approximation theory, etc., and statistics and signal processing. The Fourier transform: the continuous Fourier transform, the discrete Fourier transform, FFT, time-frequency analysis, short-time Fourier transform. The wavelet transform: the continuous wavelet transform, discrete wavelet transforms, and orthogonal bases of wavelets. Statistical estimation. Denoising by linear filtering. Inverse problems. Approximation theory: linear/nonlinear approximation and applications to data compression. Wavelets and algorithms: fast wavelet transforms, wavelet packets, cosine packets, best orthogonal bases matching pursuit, basis pursuit. Data compression. Nonlinear estimation. Topics in stochastic processes. Topics in numerical analysis, e.g., multigrids and fast solvers. Not offered 2012–13.

Credits:

9.00

Credit Hours:

Prerequisites:

ACM 11, 104, ACM 105 or undergraduate equivalent, or instructor’s permission.

Corequisites:

Exclusions:

Level:

Instructional Type:

Lecture

Notes:

Additional Information:

Historical Version(s):

Institution Website:

www.caltech.edu

Phone Number:

(626) 395-6811

Regional Accreditation:

Western Association of Schools and Colleges

Calendar System:

Quarter

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