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cgauwavf

Complex Gaussian wavelet

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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 1st 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].

example

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

The complex Gaussian function is defined as Cpe−ixe−x2. Cp is such that the 2-norm of the pth 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

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Open Live Script

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

Figure contains 2 axes objects. Axes object 1 with title Real Part contains an object of type line. Axes object 2 with title Imaginary Part contains an object of type line.

Input Arguments

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

Data Types: double

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

Data Types: double

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

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.

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

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

See Also

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