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/*Description
Compute the Complex Shannon wavelet.
The complex Shannon wavelet is defined by a bandwidth parameter fb, a wavelet center frequency fc, and the expression
psi(x) = f * b^{1/2}sinc(fb . x) e^{2 pi i f c x}
on an n-point regular grid in the interval of lb to ub.
Calling Sequence
[psi, x]= shanwavf(lb, ub, n, fb, fc)
Input Parameters
lb, ub (Real valued scalers) : Interval endpoints lb ≤ ub, specified as a pair of real-valued scalars.
n (Real valued integer strictly positive)` : Number of regularly spaced points in the interval [lb,ub], specified as a positive integer.
fb : Time-decay parameter of the wavelet (bandwidth in the frequency domain). Must be a positive scalar.
fc : Center frequency of the complex Shannon wavelet, specified as a positive scalar.
Output Parameters
psi : 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 where the complex Shannon wavelet is evaluated, returned as a 1-by-n vector. The sample points are evenly distributed between lb and ub.
Examples
1.[a,b]=shanwavf (2,8,3,1,6)
a = [-3.8982e-17 + 1.1457e-31i 3.8982e-17 - 8.4040e-31i -3.8982e-17 + 4.5829e-31i]
b = [2 5 8] */
function [psi,x]=shanwavf(lb,ub,n,fb,fc)
funcprot(0);
rhs=argn(2);
if (rhs~=5) then
error ("Wrong number of input arguments.")
else
if (n <= 0 || floor(n) ~= n)
error("n must be an integer strictly positive");
elseif (fc <= 0 || fb <= 0)
error("fc and fb must be strictly positive");
end
x = linspace(lb,ub,n);
sincx=x;
for i=1:n
sincx(i)=sin(fb*x(i)*%pi)/(fb*x(i)*%pi);
end
psi = (fb.^0.5).*(sincx.*exp(2.*%i.*%pi.*fc.*x));
end
endfunction
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