Texts

• Ronald N. Bracewell. The Fourier Transform and Its Applications. McGraw-Hill Higher Education, New York, 3d edition 2000. ISBN 0-07-303938-1. Required text for the course, ordered for the Seminary Co-op Bookstore. There is no text that really lays out the course material properly. Among the many books on transforms, this one is an efficient reference to most of the essential facts for those who apply them, and it gives a pretty nice feel for the engineer's attitude toward this sort of mathematics. The pictorial dictionary of transforms in Chapter 22 is a particularly good aid for useful reasoning with FT.
  
  
• Lecture Notes on Digital Sound Modeling. Most of the notes have to do with sound, but Chapters 1 and 4 provide basic information on complex arithmetic and Fourier Transform.
  
  
• William L. Briggs, Van Emden Henson. The DFT: An Owner's Manual for the Discrete Fourier Transform. Society for Industrial and Applied Mathematics, Philadelphia, 1995. ISBN 0-89871-342-0. I haven't had a chance to read this one yet, but it appears to cover a lot of the tricky points about the difference between continuous-infinite and discrete-finite Fourier transforms.
  
  
• Leon Cohen. Time-Frequency Analysis. Prentice-Hall PTR, Upper Saddle Hill, NJ, 1995. ISBN 0-13-594532-1. This is the de facto standard reference for time-frequency analysis. It describes the class of analysis techniques now called "Cohen's class," which covers almost everything in widespread use today.
  
  
• Athanasios Papoulis. The Fourier Integral and Its Applications. McGraw-Hill, New York, 1962. Problem 5 on page 75 gives the only printed presentation that I can find of the FT of an exponentiated quadratic. To follow the derivation you have to trace through the solution on page 77, Problem 30 on page 218 and its solution on page 220, and finally Section 9-5 on pages 186-187. Its worth it because the exponentiated quadratic is a single complex sine with amplitude varying as a Gaussian bell curve and frequency varying as a straight line. Important techniques, such as the chirp transform, depend on this sort of function. The book also presents the "principle of stationary phase" (pages 139-143) which is often used to try to illuminate time-frequency analysis.
  
  
• Ken Steiglitz. A Digital Signal Processing Primer. Addison-Wesley, 1995. ISBN 0-8053-1684-1. This is a clearly written short text on the basic methods of digital sound. I can't use it for a class text because it doesn't focus on listening experiments, and it treats the techniques a bit too uncritically. But, it could be very helpful for understanding the technicalities.
  
  

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Copyright Michael J. O'Donnell <michael_odonnell@acm.org>. Licensed for free use.
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