E: Transforms
We have already encountered various forms of the relationship between the and frequency domains. In this module, we explore the Fourier Transform and its inverse, which transform a signal between its time-domain representation and its frequency-domain representation. There are four versions, depending on whether the time-domain signal is continuous or discrete, and on whether it is periodic or aperiodic. We will be focusing on the discrete-time versions.
Required readings- Lee and Varaiya, Chapter 10 intro
- Lee and Varaiya, Section 10.1, Notation
- Lee and Varaiya, Section 10.2, The Fourier series, up to p 372
- Lee and Varaiya, Section 10.3, The discrete Fourier transform
- Lee and Varaiya, Section 10.4, The discrete-time Fourier transform
- Lee and Varaiya, Section 10.6, Fourier transforms versus Fourier series
- Generate some interesting sounds to analyze (Java applet)
http://www.cs.ubc.ca/spider/kvdoel/sound_demo6.html
- Lecture 1 :: powerpoint :: pdf
- Lecture 2 :: powerpoint :: pdf
- Questions and exercises :: pdf
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