# Digital Signal Processing

Digital signal processing is taught in the engineering curriculum, but not in the computer science or mathematics curricula. Therefore, the authors of some papers in computer vision assume substantial knowledge of digital signal processing, whereas some beginning students know next to nothing about the area.

The SPIB web page and URL directory contain pointers to on-line information resources in signal processing.

A particularly important topic in digital signal processing is the Fourier Transform, which represents a 1D signal or image as a weighted sum of sine waves. The required sine waves, together with the required weights, form a "frequency domain representation" of the image. This representation simplifies analysis of image sampling, the behavior of convolution masks, noise removal techniques, compression algorithms, and so forth.

References to the following keywords are a good clue that you might need to know some digital signal processing: sine waves, convolution, frequency domain, FFT (Fast Fourier Transform), DFT (Discrete Fourier Transform), Hartley Transform, quadrature filter, impulse response, and/or the Sampling Theorem.

Elementary, easy to read introductions to digital signal processing (in increasing order of difficulty):

• Rosen, Stuart and Peter Howell (1991) Signals and Systems for Speech and Hearing, Academic Press, London.
• Chapter 4 of Russ, John C. (1995) The Image Processing Handbook, second Edition, CRC Press (ISBN 0-8493-2516-1)
• James, J. F. (1995) A student's guide to Fourier transforms Cambridge University Press, Cambridge.

If you need to understand the details of engineering notation, particularly the design of optimal filters, see:

• Karl, John H. (1989) An Introduction to Digital Signal Processing, Academic Press, San Diego CA.

A description of the fast Fourier Transform algorithms, written in CS (rather than engineering) jargon, can be found in:

• Cormen, Thomas H., Charles E. Leiserson, and Ronald L. Rivest (1990) Introduction to Algorithms, MIT Press, Cambridge MA and McGraw-Hill, New York.

Most signal processing books consider only the 1D case in any detail. Good references for 2D digital signal processing, including computer vision applications, are

• Russ, John C. (1995) The Image Processing Handbook, second Edition, CRC Press (ISBN 0-8493-2516-1)
• Bracewell, Ronald N. (1995) Two-Dimensional Imaging, Prentice-Hall, Englewood Cliffs NJ (ISBN: 0-13-062621-X).

The discussion in Russ is easier to read and has many pictures of examples from computer vision. Bracewell covers the mathematical details and is also quite accessible.