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# cmorwavf

Complex Morlet wavelet

## Syntax

[PSI,X] = cmorwavf(LB,UB,N,FB,FC)

## Description

[PSI,X] = cmorwavf(LB,UB,N,FB,FC) returns values of the complex Morlet wavelet defined by a positive bandwidth parameter FB, a wavelet center frequency FC, and the expression

```PSI(X) = ((pi*FB)^(-0.5))*exp(2*i*pi*FC*X)*exp(-X^2/FB)
```

on an N point regular grid for the interval [LB,UB].

Output arguments are the wavelet function PSI computed on the grid X.

## Complex Morlet Wavelet

Construct a complex-valued Morlet wavelet with a bandwidth parameter of 1.5 and a center frequency of 1. Set the effective support to and the length of the wavelet to 1000.

```N = 1000;
Lb = -8;
Ub = 8;
fb = 1.5;
fc = 1;
[psi,x] = cmorwavf(Lb,Ub,N,fb,fc);
```

Plot the real and imaginary parts of the wavelet.

```subplot(2,1,1)
plot(x,real(psi)); title('Real Part');
subplot(2,1,2)
plot(x,imag(psi)); title('Imaginary Part');
```

## References

Teolis, A. (1998), Computational signal processing with wavelets, Birkhauser, p. 65.