shanwavf

Complex Shannon wavelet

Syntax

[psi,x] = shanwavf(lb,ub,n,fb,fc)

Description

[psi,x] = shanwavf(lb,ub,n,fb,fc) returns values psi of the complex Shannon wavelet evaluated on the n point regular grid in the interval [lb,ub]. The wavelet is defined by a bandwidth parameter fb and center frequency fc.

Examples

Complex Shannon Wavelet

Obtain and plot a complex Shannon wavelet. Set the bandwidth and center frequency parameters.

fb = 1;
fc = 1.5;

Set the effective support and number of sample points.

lb = -10; 
ub = 10; 
n = 1000;

Obtain the complex-valued Shannon wavelet and plot the real and imaginary parts.

[psi,x] = shanwavf(lb,ub,n,fb,fc);
tiledlayout(2,1)
nexttile
plot(x,real(psi))
title("Complex Shannon Wavelet")
xlabel("Real Part")
grid on
nexttile
plot(x,imag(psi))
xlabel("Imaginary Part")
grid on

Input Arguments

lb,ub — Interval endpoints

real-valued scalars

Interval endpoints lb ≤ ub, specified as a pair of real-valued scalars.

Data Types: double

n — Number of regularly spaced points

integer

Number of regularly spaced points in the interval [lb,ub], specified as a positive integer.

Data Types: double

fb — Bandwidth parameter

scalar

Bandwidth parameter of the complex Shannon wavelet, specified as a positive scalar.

Data Types: double

fc — Center frequency

scalar

Center frequency of the complex Shannon wavelet, specified as a positive scalar.

Data Types: double

Output Arguments

psi — Complex Shannon wavelet

vector

Complex Shannon wavelet evaluated on the n point regular grid x in the interval [lb,ub], returned as a 1-by-n vector.

x — Grid

vector

Grid where the complex Shannon wavelet is evaluated, returned as a 1-by-n vector. The sample points are evenly distributed between lb and ub.

More About

Complex Shannon Wavelet

The complex Shannon wavelet is defined as

$$\psi (x)=\sqrt{f_b}\text{sinc}(f_{b}x)\exp (2\pi i{f}_{c}x),$$

where f_b is the bandwidth parameter and f_c is the center frequency.

References

[1] Teolis, Anthony. Computational Signal Processing with Wavelets. Modern Birkhäuser Classics. Cham: Springer International Publishing, 2017. https://doi.org/10.1007/978-3-319-65747-9.

Version History

Introduced before R2006a