Trigonometrie Wavelets for Time-Frequeney-Analysis
Kathi Selig · 1995
We present here a new solution for the problem of periodic time-frequency-Iocalized signal analysis. Working on polynomials with Fourier coefficients included in bands similar to octaves, we can vary the actual position and length of those bands and also the localization of the bases in the time domain by the choice of parameters. Having simple, fast and numerically stable algorithms, this concept can be easily applied to various practical tasks. 1 Introduetion For trigonometrie polynomials P E Tn of degree at most n (n E N), we have two kinds of representations. The first one is the Fourier series n p(x) = SnP(x) E Ck(P) e ikx ,