MORSEXPAND Generalized Morse wavelets via time-domain Taylor series. PSI=MORSEXPAND(T,GAMMA,BETA,FS) computes the lowest-order generalized Morse wavelet specified by parameters GAMMA and BETA, and having a peak frequency at *radian* frequency FS, using a time-domain Taylor series. Normally one would use MORSEWAVE to compute the wavelets in the frequency domain, but it is sometimes useful to have an explicit time-domain representation. There are no contraints on the size of T nor its ordering. All input parameters other than T should be scalars. __________________________________________________________________ Algorithms MORSEXPAND can use one of two different algorithms. MORSEXPAND(,...,'moment'), the default behavior, Taylor-expands the time-domain wavelet directly. MORSEXPAND(,...,'cumulant') expands the logarithm of the time-domain wavelet and then takes the exponential. MORSEXPAND(N,...) specifies the number of terms to include in the Taylor expansion. N defaults to 10 in the 'cumulant' case and 100 in the 'moment' case. These algorithms implement equations (30) and (31) of Lilly and Olhede (2009). For details see Lilly and Olhede (2009). Higher-order properties of analytic wavelets. IEEE Trans. Sig. Proc., 57 (1), 146--160. __________________________________________________________________ See also MORSEWAVE, WAVETRANS. 'morsexpand --t' runs a test. Usage: psi=morsexpand(t,gamma,beta,fs); psi=morsexpand(n,t,gamma,beta,fs); __________________________________________________________________ This is part of JLAB --- type 'help jlab' for more information (C) 2007--2016 J.M. Lilly --- type 'help jlab_license' for details