Foundations of Signal Processing

Goyal, Kovacevic, and Vetterli wrote:Our main goals in this book and its companion volume, Fourier and Wavelet Signal Processing (FWSP) [57], are to enable an understanding of state-of-the-art signal processing methods and techniques, as well as to provide a solid foundation for those hoping to advance the theory and practice of signal processing. We believe that the best way to grasp and internalize the fundamental concepts in signal processing is through the geometry of Hilbert spaces, as this leverages the great innate human capacity for spatial reasoning. While using geometry should ultimately simplify the subject, the connection between signals and geometry is not innate. The reader will have to invest effort to see signals as vectors in Hilbert spaces before reaping the benefits of this view; we believe that effort to be well placed.