This textbook for undergraduate mathematics, science, and engineering students introduces the theory and applications of discrete Fourier and wavelet transforms using elementary linear algebra, without assuming prior knowledge of signal processing or advanced analysis.
It explains how to use the Fourier matrix to extract frequency information from a digital signal and how to use circulant matrices to emphasize selected frequency ranges. It introduces discrete wavelet transforms for digital signals through the lifting method and illustrates through examples and computer explorations how these transforms are used in signal and image processing. Then the general theory of discrete wavelet transforms is developed via the matrix algebra of two-channel filter banks. Finally, wavelet transforms for analog signals are constructed based on filter bank results already presented, and the mathematical framework of multiresolution analysis is examined.
Sample Chapter(s)
Chapter 1: Linear Algebra and Signal Processing (405 KB)
Errata(s)
Errata (224 KB)
Contents:
- Linear Algebra and Signal Processing
- Discrete Fourier Transform
- Discrete Wavelet Transforms
- Wavelet Transforms from Filter Banks
- Wavelet Transforms for Analog Signals
- Appendix A: Some Mathematical and Software Tools
- Appendix B: Solutions to Exercises
Readership: Undergraduate mathematics, science and engineering students interested in the theory and applications of discrete Fourier and wavelet transforms.
