📄 s_spectrum2wavelet.m
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function wavelet=s_spectrum2wavelet(freq,amps,varargin)
% Compute wavelet from its amplitude spectrum
% Written by: E. R.: November 27, 2004
% Last updated:
%
% wavelet=s_spectrum2wavelet(freq,amps,varargin)
% INPUT
% freq frequency values at which the spectrum is defined
% amps associated values of the amplitude spectrum
% varargin one or more cell arrays; the first element of each cell array is a keyword,
% the other elements are parameters. Presently, keywords are:
% 'step' sample interval of the seismic
% Default: {'step',4}
% 'wlength' wavelet length
% Default: {'wlength',100}
% 'dc_removal' should DC be removed. Possible values: 'yes' and 'no'.
% Default: {'dc_removal','yes'}
% OUTPUT
% wavelet zero-phase wavelet with spectrum defined by "freq" and "amps".
%
% EXAMPLE
% wavelet=s_spectrum2wavelet([10,20,40,60],[0,1,1,0],{'wlength',80})
% s_spectrum(wavelet)
% Set deafaults of input arguments
param.step=4;
param.wlength=100;
param.method='linear';
param.dc_removal='yes';
% Replace defaults by input parameters
param=assign_input(param,varargin);
nsamp=odd(param.wlength/param.step);
ansamp1=nsamp-1;
awlength=ansamp1*param.step;
% Wavelet length used for spectrum interpolation
nsamp1=4*ansamp1;
nsamp=nsamp1+1;
wlength=nsamp1*param.step;
% Sample interval in the frequency domain
equidist=(0:2:nsamp)*500/(param.step*nsamp);
freq=[0;freq(:);equidist(end)];
amps=[0;amps(:);0];
[freq,index]=unique(freq);
amps=amps(index);
aspectrum=reshape(interp1(freq,amps,equidist,param.method),[],1);
aspectrum=[aspectrum;aspectrum(end:-1:2)];
wavelet.type='seismic';
wavelet.tag='wavelet';
wavelet.name='Wavelet with defined spectrum';
wavelet.first=-awlength/2;
wavelet.last=-wavelet.first;
wavelet.step=param.step;
wavelet.units='ms';
traces=fftshift(real(ifft(aspectrum)));
inc=(nsamp1-ansamp1)/2;
wavelet.traces=traces(inc+1:end-inc);
wavelet.traces([1,end])=wavelet.traces([1,end])*0.5;
if strcmpi(param.dc_removal,'yes')
wavelet.traces=wavelet.traces-sum(wavelet.traces)/(length(wavelet.traces)-1);
end
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
function m=odd(m)
m=2*round((m-1)*0.5)+1;
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