MORSEMOM Frequency-domain moments of generalized Morse wavelets. MORSEMOM is a low-level function called by several other Morse wavelet functions. [MP,NP]=MORSEMOM(P,GAMMA,BETA) computes the Pth order frequency- domain moment M and energy moment N of the lower-order generalized Morse wavelet specified by parameters GAMMA and BETA. The Pth moment and energy moment are defined as mp = 1/(2 pi) int omega^p psi(omega) d omega np = 1/(2 pi) int omega^p |psi(omega)|.^2 d omega respectively, where omega is the radian frequency. These are evaluated using the 'bandpass' normalization, which has max(abs(psi(omega)))=2. The input parameters must either be matrices of the same size, or some may be matrices and the others scalars. [MP,NP,KP,LP]=MORSEMOM(...) also returns the Pth order cumulant KP and the Pth order energy cumulant LP. Note that for very large BETA, the standard form of the moments fail for numerical reasons, and one must use asymptotic forms. These are used by default when the argument to the gamma function exceeds 100 and when then standard expressions yield non-finite or zero values. For details see Lilly and Olhede (2009). Higher-order properties of analytic wavelets. IEEE Trans. Sig. Proc., 57 (1), 146--160. See also MORSEWAVE, MORSEDERIV, MOM2CUM. 'morsemom --t' runs some tests. Usage: mp=morsemom(p,ga,be); [mp,np]=morsemom(p,ga,be); [mp,np,kp,lp]=morsemom(p,ga,be); __________________________________________________________________ This is part of JLAB --- type 'help jlab' for more information (C) 2007--2021 J.M. Lilly --- type 'help jlab_license' for details