[PSI,X] = gauswavf(LB,UB,N)
[PSI,X] = gauswavf(LB,UB,N,P)
[PSI,X] = gauswavf(LB,UB,N,WAVNAME)
[PSI,X] = gauswavf(LB,UB,N) returns the
1st order derivative of the Gaussian wavelet,
N-point regular grid,
for the interval
[LB,UB]. The effective support
of the Gaussian wavelets is
[PSI,X] = gauswavf(LB,UB,N,P) returns the
Valid values of
P are integers from 1 to 8.
The Gaussian function is defined as . Cp is
such that the 2-norm of the
PSI is equal to 1.
[PSI,X] = gauswavf(LB,UB,N,WAVNAME) uses
the valid wavelet family short name
the order of the derivative in a character vector, such as
To see valid character vectors for Gaussian wavelets, use
wavemngr('read',1) and refer to the Gaussian
For visualizing the second or third order derivative of Gaussian wavelets, the convention is to use the negative of the normalized derivative. In the case of the second derivative, scaling by -1 produces a wavelet with its main lobe in the positive y direction. This scaling also makes the Gaussian wavelet resemble the Mexican hat, or Ricker, wavelet. The validity of the wavelet is not affected by the -1 scaling factor.
% Set effective support and grid parameters. lb = -5; ub = 5; n = 1000; % Compute Gaussian wavelet of order 8. [psi,x] = gauswavf(lb,ub,n,8); % Plot Gaussian wavelet of order 8. plot(x,psi), title('Gaussian wavelet of order 8'), grid