TY - BOOK ID - 7249243 TI - Time-frequency representations. AU - Myoung, An AU - Tolimieri, Richard PY - 1998 SN - 3764339187 0817639187 146128676X 1461241529 9783764339180 9780817639181 PB - Boston Birkhäuser DB - UniCat KW - Signal processing KW - Time-series analysis KW - Frequency spectra KW - Mathematics KW - 517.518 KW - 681.3*G12 KW - Metric theory of functions KW - Approximation: chebyshev; elementary function; least squares; linear approximation; minimax approximation and algorithms; nonlinear and rational approximation; spline and piecewise polynomial approximation (Numerical analysis) KW - 681.3*G12 Approximation: chebyshev; elementary function; least squares; linear approximation; minimax approximation and algorithms; nonlinear and rational approximation; spline and piecewise polynomial approximation (Numerical analysis) KW - 517.518 Metric theory of functions KW - Abelian groups KW - Analysis of time series KW - Autocorrelation (Statistics) KW - Harmonic analysis KW - Mathematical statistics KW - Probabilities KW - Spectra, Frequency KW - Spectrum, Frequency KW - Spectrum analysis KW - Commutative groups KW - Group theory KW - Computer mathematics. KW - Signal processing. KW - Image processing. KW - Speech processing systems. KW - Applied mathematics. KW - Engineering mathematics. KW - Computational Mathematics and Numerical Analysis. KW - Signal, Image and Speech Processing. KW - Computational Science and Engineering. KW - Applications of Mathematics. KW - Processing, Signal KW - Information measurement KW - Signal theory (Telecommunication) KW - Engineering KW - Engineering analysis KW - Mathematical analysis KW - Computational linguistics KW - Electronic systems KW - Information theory KW - Modulation theory KW - Oral communication KW - Speech KW - Telecommunication KW - Singing voice synthesizers KW - Pictorial data processing KW - Picture processing KW - Processing, Image KW - Imaging systems KW - Optical data processing KW - Computer mathematics KW - Electronic data processing KW - Abelian groups. KW - Frequency spectra. KW - Signal processing - Mathematics UR - https://www.unicat.be/uniCat?func=search&query=sysid:7249243 AB - The aim of this work is to present several topics in time-frequency analysis as subjects in abelian group theory. The algebraic point of view pre­ dominates as questions of convergence are not considered. Our approach emphasizes the unifying role played by group structures on the development of theory and algorithms. This book consists of two main parts. The first treats Weyl-Heisenberg representations over finite abelian groups and the second deals with mul­ tirate filter structures over free abelian groups of finite rank. In both, the methods are dimensionless and coordinate-free and apply to one and multidimensional problems. The selection of topics is not motivated by mathematical necessity but rather by simplicity. We could have developed Weyl-Heisenberg theory over free abelian groups of finite rank or more generally developed both topics over locally compact abelian groups. However, except for having to dis­ cuss conditions for convergence, Haar measures, and other standard topics from analysis the underlying structures would essentially be the same. A re­ cent collection of papers [17] provides an excellent review of time-frequency analysis over locally compact abelian groups. A further reason for limiting the scope of generality is that our results can be immediately applied to the design of algorithms and codes for time­ frequency processing. ER -