cgauwavf

Complex Gaussian wavelet

Syntax

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

[psi,x] = cgauwavf(lb,ub,n,p)

[psi,x] = cgauwavf(lb,ub,n,wname)

Description

[psi,x] = cgauwavf(lb,ub,n) returns the 1^st order derivative of the complex-valued Gaussian wavelet, psi, on an n-point regular grid, x, for the interval [lb,ub]. The effective support of the complex-valued Gaussian wavelets is [-5, 5].

[psi,x] = cgauwavf(lb,ub,n,p) returns the p^th derivative. p is an integer from 1 through 8.

The complex Gaussian function is defined as $$C_p{e}^{-ix}{e}^{-x^2}$$. C_p is such that the 2-norm of the p^th derivative of psi is equal to 1.

[psi,x] = cgauwavf(lb,ub,n,wname) used the valid wavelet family short name wname plus the order of the derivative in a character vector or string scalar, such as 'cgau4'. To see valid character vectors for complex-valued Gaussian wavelets, use waveinfo('cgau') or use wavemngr('read',1) and refer to the Complex Gaussian section.

Examples

Create Complex Gaussian Wavelet

This example shows how to create a complex-valued Gaussian wavelet of order 4. The wavelet has an effective support of [-5,5] and is constructed using 1,000 samples.

lb = -5; 
ub = 5; 
n = 1000;
order = 4;
[psi,x] = cgauwavf(lb,ub,n,order);
subplot(2,1,1)
plot(x,real(psi))
title('Real Part')
grid on
subplot(2,1,2)
plot(x,imag(psi))
title('Imaginary Part')
grid on

Input Arguments

lb — Left endpoint

real number

Left endpoint of the closed interval, specified as a real number. lb is strictly less than ub.

Data Types: double

ub — Right endpoint

real number

Right endpoint of the closed interval, specified as a real number. ub is strictly greater than lb.

Data Types: double

n — Number of regularly spaced points

positive integer

Number of regularly spaced points in the interval [lb,ub], specified as a positive integer. The derivative of the complex-valued Gaussian wavelet is evaluated at these points.

Data Types: double

p — Derivative

positive integer

Positive integer defining the order of the derivative of the complex-valued Gaussian, specified as a positive integer. p is an integer from 1 through 8.

wname — Gaussian wavelet

character vector | string scalar

Gaussian wavelet to evaluate, specified as a character vector or string scalar. wname is of the form 'cgauN' where N is an integer that denotes the order of the derivative of the complex-valued Gaussian. N is an integer from 1 through 8.

Example: 'cgau4' denotes the fourth derivative of the complex-valued Gaussian wavelet.

Output Arguments

psi — Derivative of complex-valued Gaussian wavelet

complex-valued vector

Derivative of the complex-valued Gaussian wavelet, returned as a complex-valued 1-by-N vector.

x — Sample points

real-valued vector

Sample points where the derivative of the complex-valued Gaussian wavelet is evaluated, returned as a real-valued 1-by-N vector. The sample points are evenly distributed between lb and ub.

Version History

Introduced before R2006a