# MORLWAVE is the jWavelet module of jLab.

``` MORLWAVE  Morlet wavelet.

The Morlet wavelet is not recommended.  Instead use a generalized Morse
wavelet with GAMMA set to 3.  This function is included for testing and
comparison purposes.  See Lilly and Olhede (2009, 2012) for details.

PSI=MORLWAVE(N,FMAX,F) returns the complex-valued Morlet wavelet of
length N, with a peak in the frequency domain at *radian* F, based on a
mother wavelet having a peak frequency FMAX>1.

If F is a scalar, PSI is a column vector of length M.  If F is an
array, PSI is a matrix of size M x LENGTH(F), with the columns in order
of decreasing frequency.

The peak frequency FMAX should be greater than one.  As FMAX increases
from unity, the number of oscillations in the wavelet increases.

Note that the wavelets are centered at the midpoint in time, row
number ROUND(SIZE(PSI,1)/2).

[PSI,PSIF]=MORLWAVE(N,FMAX,F) also returns a size SIZE(PSI) matrix
PSIF which is the frequency-domain version of the wavelets.

For further details on this representation of the Morlet wavelet, see
Appendix A of

Lilly and Olhede (2009).  Higher-order properties of analytic
wavelets.  IEEE Trans. Sig. Proc., 57 (1), 146--160.
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Normalization

MORLWAVE supports two kinds of normalization for the wavelets.

MORLWAVE(..., 'bandpass') uses "bandpass normalization", the
default.  See Lilly and Gascard (2006).  This implies that the
FFT of wavelet has a maximum value of 2.

MORLWAVE(..., 'energy') uses the unit energy normlization.  The
time-domain wavelet energy SUM(ABS(PSI).^2) is then unity.

Note MORLWAVE now uses bandpass-normalization by default.
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