CMSC 34910
Transforms for Signal ProcessingPrerequisites: Differential and integral calculus, sine and cosine functions, addition, subtraction, multiplication, division and exponentiation of complex numbers
Catalog Description: We study the use of mathematical transforms to reveal the frequency or scale structure of signals, such as vibrations and visual scenes. We cover the continuous and discrete Fourier, wavelet, Laplace, and Z transforms, and others if time permits. We do not prove the relevant mathematical theorems: we state them and use them to calculate and reason rigorously about interesting properties of signals, and about transformations of signals by filters. We explore the pitfalls of naive applications of transforms. Finally, we study recent research articles on frameless time-frequency analysis. Students are not required to program in a general-purpose programming language. They are required to perform computational exercises using an interactive numerical system such as Octave (Matlab) or Scilab.
Long Description: We study the use of mathematical transforms to reveal the frequency or scale structure of signals, such as vibrations and visual scenes. We cover the continuous and discrete Fourier, wavelet, Laplace, and Z transforms, and others if time permits. We do not prove the relevant mathematical theorems: we state them and use them to calculate and reason rigorously about interesting properties of signals, and about transformations of signals by filters.
The text provides most of the basic information. We go well beyond the text in exploring the pitfalls of naive applications of transforms. A student who completes the course successfully can apply mathematical transforms entirely correctly, paying attention to phase as well as magnitude, and recognizing the confusion introduced by framing and discretization. Finally, we study recent research articles on frameless time-frequency analysis.
Students are not required to program in a general-purpose programming language. They are required to perform computational exercises using an interactive numerical system such as Octave (Matlab) or Scilab.
Text: Ronald N. Bracewell, The Fourier Transform and Its Applications
Instructors: Michael O'DonnellQuarter offered: WIN
Last Verified by Sharon Salveter on 16 September, 2004.