The mathematics of signal processing Preface Introduction 1. Normed vector spaces 2. Analytic tools 3. Fourier series 4. The Fourier transform 5. Compressive sampling 6. Discrete transforms 7. Linear filters 8. Windowed fourier and continuous wavelet transforms. Frames 9. Multiresolution analysis 10. Discrete wavelet theory 11. Biorthogonal filters and wavelets 12. Parsimonious representation of data