# SLIDETRANS is the jSpectral module of jLab.

``` 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.
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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.
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'slidetrans --t' runs a test.
'slidetrans --f' generates a sample figure.

Usage: y=slidetrans(x,psi,f);
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This is part of JLAB --- type 'help jlab' for more information
(C) 2004--2015 J.M. Lilly --- type 'help jlab_license' for details
```