fftnoise - generate noise with a specified power spectrum

Useful helper function for Monte Carlo null-hypothesis tests and confidence interval estimation.

Description

USAGE: noise=fftnoise(f[,Nseries])
 

INPUTS:
  f: the fft of a time series (must be a column vector)
  Nseries: number of noise series to generate. (default=1)
  
OUTPUT:
  noise: surrogate series with same power spectrum as f. (each column is a surrogate).

  ------ Example: ------
  %calculate if the trend is significantly different from zero
  %(Null-hypothesis: a random process with the same power spectrum as data).
 
  x=(1:100)';
  data=smooth(randn(size(x)),15);
  pdata=polyfit(x,data,1)
  f=fft(data);
  psur=nan(length(pdata),10000);
  for ii=1:size(psur,2)
    psur(:,ii)=polyfit(x,fftnoise(f),1)';
  end
  ptile=prctile(psur(1,:)',[2.5 97.5])
  if (pdata(1)>ptile(2))|(pdata(1)<ptile(1))
    disp('significant trend')
  else
    disp('not significant trend')
  end

• MATLAB release: MATLAB 6.0 (R12)
• Other requirements: [ statistics toolbox (prctile.m) is necessary for the listed example ]