[R] Inverse transform after applying function in frequency domain?

From: Keith Alan Chamberlain <Keith.Chamberlain_at_Colorado.EDU>
Date: Sat, 19 Apr 2008 04:30:49 -0600


Dear R-Help,

I wish to simulate a process so that it has certain properties in the frequency domain. What I attempted was to generate a random time-series signal, use spec-pgram(), apply a function in the frequency domain, and then inverse transform back to the time-domain. This idea does not seem as straight forward in practice as I anticipated.

e.g.
x<-ts(rnorm(1000, 0,1), frequency=256)

plot(x)				## looks like noise.
pgm<-spec.pgram(x, taper=0)	## a flat spectra, white noise
fx<-pgm$freq^(-1)+pgm$spec	## apply a function
plot(log(fx)~log(pgm$freq))	## scaling properties
x2<-fft(fx, inverse=T)
plot(Re(x2))			## not quite what I intended

. Which, although I get some fantastic looking plots, isn't quite what I anticipated. How do I apply a function or filter in the frequency domain, then inverse transform to the scale of my original time series?

Sincerely,
KeithC.
Psych Undergrad, CU Boulder
RE McNair Scholar [U.S]

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