The goal of this course is to introduce the students to the modern mathematical techniques which are applied in signal processing and which are used in a variety of areas, ranging from engineering to medicine and finance. Topics include: Applied Linear Algebra, Fourier Series, Discrete Fourier Transform, Fourier Transform, Shannon Sampling Theorem, Wavelet Bases, Multiresolution Analysis, and Discrete Wavelet Transform. Emphasis will be placed upon mathematical foundations of applicable algorithms, as well as on the ability to implement these algorithms.
MATH 141; MATH 240 or MATH461 or MATH341. Familiarity with MATLAB is also required.
Background Material: Numbers and Computer Arithmetic, Vector Spaces and Linear Transformations; Fourier Series; Discrete Fourier Transform; Sampling; Quantization; Precision and Accuracy; Wavelet Bases; Discrete Wavelet Transform; Applications to Coding, Detection, and Compression.