function [w_min] = kolmog(w,type_of_input,L);  %KOLMOG: Kolmogoroff spectral factorization.%        Given an arbitrary wavelet this function retrieves the minimum %        phase wavelet using Kolmogoroff factorization.%%  %  [w_min] = kolmog(w,type_of_input,L)%%  IN   w:     a wavelet of arbitrary phase %              or seismic trace (column vector)%              type_of_input = 'w': wavelet%              type_of_input = 't': seismic trace%              L: lenght of wavelet if type_of_input='t'%%  OUT  w_min: a min phase wavelet %%%  Example:%            w = [1,2]';   %            w_min = kolmog(w);  % %%  Author(s): M.D.Sacchi (sacchi@phys.ualberta.ca)%  Copyright 1998-2003 SeismicLab%  Revision: 1.2  Date: Dec/2002 %  %  Signal Analysis and Imaging Group (SAIG)%  Department of Physics, UofA%[n1,n2]=size(w);if n2~=1; error('Input wavelet or trace must be a column vector');end;if isequal(type_of_input,'w')nw = length(w);    % lenght of the waveletnfft = 8*( 2^nextpow2(nw));W = log ( abs(fft(w,nfft)) +0.00001);W = ifft(W);for k=nfft/2+2:nfft; W(k)=0.;end;W = 2.*W;W(1) =W(1)/2.;W = exp(fft(W)) ;w_min = real(ifft(W));w_min = w_min(1:nw); else;nt = length(w);    % size of the tracenfft = 8*( 2^nextpow2(nt));nw = L;A = xcorr(w,w,L);A = A.*hamming(2*L+1);W = log ( sqrt(abs(fft(A,nfft))) +0.00001);W = ifft(W);for k=nfft/2+2:nfft; W(k,1)=0.;end;W = 2.*W;W(1,1) =W(1,1)/2.;W = exp(fft(W)) ;w_min = real(ifft(W));w_min = w_min(1:nw,1); w_min_max = max(abs(w_min));w_min = w_min/w_min_max;end;return