Discrete Fourier Analysis (Paperback)

Preface.- The Finite Fourier Transform.- Translation-Invariant Linear Operators.- Circulant Matrices.- Convolution Operators.- Fourier Multipliers.- Eigenvalues and Eigenfunctions.- The Fast Fourier Transform.- Time-Frequency Analysis.- Time-Frequency Localized Bases.- Wavelet Transforms and Filter Banks.- Haar Wavelets.- Daubechies Wavelets.- The Trace.- Hilbert Spaces.- Bounded Linear Operators.- Self-Adjoint Operators.- Compact Operators.- The Spectral Theorem.- Schatten?von Neumann Classes.- Fourier Series.- Fourier Multipliers on S¹.- Pseudo-Differential Operators on S¹.- Pseudo-Differential Operators on Z.- Bibliography.- Index.