G: Fourier Analysis
This module quickly reviews the four Fourier Transforms, and then proceeds to explore topics based on them, such as spectral analysis of time-varying signals.Required readings
- Lee and Varaiya, Chapter 10, The four Fourier transforms
- Kadi, Session 8, Spectral Analysis
- Smith, Chapter 9, Applications of the DFT
http://www.dspguide.com/ch9.htm - Smith, Chapter 18, FFT Convolution
http://www.dspguide.com/ch18.htm
- Extract a portion of a music signal from a CD. (To ensure copyright conformance, do not redistribute the resulting files.) Generate different analyses of the frequency content, and analyze it.
- Do the same for a different genre of music (jazz, classical, baroque, funk, rock, etc). Compare it with the previous sample.
- Do the same for a movie soundtrack with effects on it (explosions and so on). Compare and contrast.
- Using FFT convolution, alter the frequency content of one of the above samples.
- Write and explain the mathematics of the above.
- Lee and Varaiya, Lab 7. Spectrum.
- Lee and Varaiya, Lab 8. Comb filters.
- Fourier transform, Wikipedia
http://en.wikipedia.org/wiki/Fourier_transform