[R] Complex demodulation - Purely a time series question

[Brian Scholl]

Hi, this is purely a time series question if anyone has a hint.

I'm trying to complex demodulate a series at different frequencies. Say at
$\lambda$ = 1/100, 1/41 and 1/23.  (These correspond to various astronomical
forcing frequencies of ice ages, incidentally).

Now, following say Hasan (1982, Hand. of Stats) or Brillinger (1987, Fitting
Cosines), I do the following:
1. from y, form the series y(t)*exp(i*lambda*t)
2. take the log of the modulus of the new series
When I'm done, I should be able to plot the series as a function of time and
get a sense of the amplitude of the harmonic signal at the frequency I'm
interested in.

Well, I do this, but the plots for different frequencies are darn near
identical.  This does not seem reasonable because: the periodogram detects a
strong peak at 100kyrs, but not at 23 kyrs; and knowledge of the data
suggests the demodulated series should look different.  On the other side,
1/100 and 1/23 aren't hugely different - but then what's really the point of
isolating the frequency?

I know this is a cross listing, but any help would be appreciated.  Thanks.

Some code:

    t<-1:length(y)
    yt<-(y*exp(1i*(.01)*t))
#    yt=smoother(yt,5,t,1);
    demod100<-log(abs(yt));
    phase100<-Arg(yt);


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