R/FRWDft.R

In RSEIS: Seismic Time Series Analysis Tools

`FRWDft` <-
function(g,n,tstart,dt)
  {

#####%   FRWDft            Fourier Transform with time shift and sample interval scaling
#####% USAGE: [G,f,t]=FRWDft(g,n,tstart,dt);
#####% Compute the Fourier Transform of g(t) correcting for time offsets and sample
###% interval.  Output is scaled using conventions of continuous transforms in
###% Aki and Richards and in J.H. Karl.
###%
###% INPUT: g is a column vector time series evaluated at times specified by
###%        tstart and dt.  if tstart is a vector, it is the time vector and
###%        dt is not necessary. if tstart is a scalar, it is the start time
###%        and the sample interval is dt.  n is the number of points in the FFT.
###%        g is truncated or zero-padded to n points.
###%
###% OUTPUT: G is the Fourier Transform of g.  it is scaled by dt to be
###%        consistent with the continuous transform.  the time shift
###%        theorem has been used to account for time not starting at t=0.
###%        the length of G is n.
###%        f is the frequency vector for G.
###%        t is the time vector for g.
###%
###% See also INVRFT and MAKEFREQ.

###% adapted and translated from K. Creager  kcc@geophys.washington.edu   12/30/93
########  modified by J. M. Lees 10/20/2007

                   
    N=length(g)                    #% length of input time-domain vector
    if(length(tstart)>1 )
      {
                                        #% define time vector
        t=tstart;
        tstart=t(1);
        dt=t(2)-t(1);
      }
    else
      {
        t=tstart+seq(from=0,by=dt,to=(N-1)*dt)    #% time vector
      }


if(length(t)!=N)
  {
  ### error('size of time and data vectors must be the same in FRWDFT')
  }

    f=makefreq(N,dt);                    #% construct the frequency vector
    i = complex(real=0, imaginary=1)   
    G=dt*fft(g)*exp(-2*pi*i*tstart*f)
                                        #% forward fourier transform with time shift
    return(list(G=G, f=f, t=t))
}