specshift.m

Spectral Element Method for wave propagation and rupture dynamics.

%datout = specshift(signal,shift)
%
% PURPOSE:	Subsample time-shift of real data
%		via phase shift in spectral domain 
%
% INPUT:	signal	in principle the input must be band-limited
%			to < Nyquist frequency (1/2 sampling frequency)
%			=> preprocess by taper then low-pass filter
%			(this is usually done by the instrument anti-alias filter)
%			If matrix: signal(time,index)
%		shift	in sample units (can be non-integer, vector)
%

function datout = specshift(datin,shift)

if any(size(datin)==1), datin = datin(:); end
shift=shift(:);

nshift = length(shift);
[Nin,nsis] = size(datin);
if nshift>1 & nsis>1 & nshift~=nsis, error('arguments have wrong size'); end

N = 2^(nextpow2( Nin +max(abs(shift)) )); % +? to avoid wraparound
fdatin = fft(datin,N);

ik = 2i*pi*(0:N/2).'/N; 
ik(N/2+2:N)=-ik(N/2:-1:2);

if nsis==1 & nshift==1
  
  fshift = exp(ik*shift) ;
  fshift(N/2+1)=real(fshift(N/2+1)); 	% must be real at the Nyquist frequency (-> output is real),
  					% although irrelevant when the input has been low-pass filtered
  datout = real(ifft(fshift .*fdatin));
  datout = datout(1:Nin) ;
  
else
  
  fshift = exp(ik*shift') ;  % [N,ns]
  if nsis==1 & nshift>1, fdatin = repmat(fdatin,1,nshift); end
  if nshift==1 & nsis>1, fshift = repmat(fshift,1,nsis);   end
  fshift(N/2+1,:)=real(fshift(N/2+1,:));
  fshift = fshift.*fdatin;
  datout = real(ifft( fshift ));
  datout = datout(1:Nin,:);
  
end