02238nmm a2200265 u 4500001001200000003002700012005001700039007002400056008004100080020001800121050001300139100002300152245008000175260004800255300002800303505041000331653003600741700003000777041001900807989003200826490004300858856006300901082001700964520099100981EB001887944EBX0100000000000000105130500000000000000.0cr|||||||||||||||||||||200106 ||| eng a9781139003896 4aTK5102.91 aDamelin, Steven B.00aThe mathematics of signal processingcSteven B. Damelin, Willard Miller, Jr aCambridgebCambridge University Pressc2012 axii, 449 pagesbdigital0 aPreface -- 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 aSignal processing / Mathematics1 aMiller, Willarde[author]07aeng2ISO 639-2 bCBOaCambridge Books Online0 aCambridge texts in applied mathematics40uhttps://doi.org/10.1017/CBO9781139003896xVerlag3Volltext0 a621.38220151 aArising from courses taught by the authors, this largely self-contained treatment is ideal for mathematicians who are interested in applications or for students from applied fields who want to understand the mathematics behind their subject. Early chapters cover Fourier analysis, functional analysis, probability and linear algebra, all of which have been chosen to prepare the reader for the applications to come. The book includes rigorous proofs of core results in compressive sensing and wavelet convergence. Fundamental is the treatment of the linear system y=Φx in both finite and infinite dimensions. There are three possibilities: the system is determined, overdetermined or underdetermined, each with different aspects. The authors assume only basic familiarity with advanced calculus, linear algebra and matrix theory and modest familiarity with signal processing, so the book is accessible to students from the advanced undergraduate level. Many exercises are also included