SLIDETRANS Sliding-window ('moving-window') Fourier transform. Y=SLIDETRANS(X,PSI,F) computes the sliding-window Fourier transform of the signal X using window PSI at frequencies F. X and W are column vectors. Y is a matrix of size LENGTH(X) by LENGTH(FS). The frequencies F are radian frequencies as in COS(F T). PSI may also be a matrix, in which case Y is a 3-D array of size LENGTH(X) by LENGTH(FS) by SIZE(W,2). SLIDETRANS(...,STR) sets the endpoint boundary conditions, with STR equal to 'mirror', 'periodic', or 'zeros'. The default is 'periodic'. For more details, see the boundary condition discussion in WAVETRANS. A good choice for window is the first "Slepian" taper; see SLEPTAP. Hermite functions are also used; see HERMFUN. SLIDETRANS follows the same normalization as WAVETRANS when the input signal X is complex-valued, so see that function for details. _________________________________________________________________ Definition The sliding window transform is defined as y(t,f) = int psi^*(u-t) exp[-2 pi i f (u-t)] x(t) du. When a sinusoid is transformed at its own frequency, the rate of change of the phase of the sliding window transform recovers the frequency of the sinusoid. This is the same as with the wavelet transform. This differs from the definition of Mallat (1999), p. 69, by a unit amplitude factor of exp[2 pi i f t]. In Mallat's defintion, the transform of a sinusoid at the sinusoid's frequency has constant phase. Both definitions have the same modulus. _________________________________________________________________ 'slidetrans --t' runs a test. 'slidetrans --f' generates a sample figure. Usage: y=slidetrans(x,psi,f); _________________________________________________________________ This is part of JLAB --- type 'help jlab' for more information (C) 2004--2015 J.M. Lilly --- type 'help jlab_license' for details