morlet

Morlet wavelet

Syntax

[psi,x] = morlet(lb,ub,n)

Description

[psi,x] = morlet(lb,ub,n) returns the Morlet wavelet psi evaluated at x, an n-point regular grid in the interval [lb, ub]. The Morlet wavelet is defined as

The Morlet wavelet has the interval [-4, 4] as effective support. Nearly 100% of the wavelet's energy is in the interval. Although [-4, 4] is the correct theoretical effective support, a wider effective support, [-8, 8], is used in the computation to provide more accurate results.

Examples

Morlet Wavelet

This example shows how to create a Morlet wavelet. The wavelet has an effective support of [-4, 4]. Use 1000 sample points.

lb = -4;
ub = 4;
n = 1000;
[psi,xval] = morlet(lb,ub,n);
plot(xval,psi)
grid on
title('Morlet Wavelet')

Compute the wavelet's energy in the interval. Normalize by the difference between sample points.

e1 = sum(psi.^2)*diff(xval(1:2));
fprintf('%.15f',e1)

0.886226920745597

Create a second Morlet wavelet with support on [-8, 8] using 1000 sample points. Compute the second wavelet's energy, normalized by the difference between sample points. Return the ratio of the two energies.

[psi2,xval2] = morlet(-8,8,1000);
e2 = sum(psi2.^2)*diff(xval2(1:2));
fprintf('%.15f',e1/e2)

0.999999994674672

Input Arguments

lb — Lower limit

real-valued scalar

Lower limit of interval, specified as a real-valued scalar.

ub — Upper limit

real-valued scalar

Upper limit of interval, specified as a real-valued scalar.

n — Number of points

positive integer

Number of sample points, specified as a positive integer.

Output Arguments

psi — Morlet wavelet

real-valued vector

Morlet wavelet, returned as a real-valued vector of length n.

x — Sampling instants

real-valued vector

Sampling instants, returned as a real-valued vector of length n.

Version History

Introduced before R2006a