linear interpolation of a log-time sequence
- From: "Robert Adams" <robert.adams@xxxxxxxxxx>
- Date: 17 Aug 2005 17:29:39 -0700
The following is really a signal-processing question that appears here
because it goes well beyond standard "math for engineers".
Suppose that I have a finite-length sequence of weighted time-domain
impulses (Dirac functions) that occur on a log-time grid Tn = log(n), n
an integer from 1 to K where K is the sequence length, and with a
weighting factor w(n).
One can numerically compute the Fourier transform in any particular
case by the simple summation of exponentials of the form
w(n)*exp(-i*w*log(n)) from n=1 to K.
I need to interpolate this sequence to a LINEAR time grid Tn = n, in
such a way as to preserve the magnitude of the Fourier Transform below
the Nyquist rate (w < PI). Since the effective sampling rate of the
log-time sequence is increasing over time, it is obvious that the FT of
the linearly-interpolated sequence can only match below w = PI.
One approach would be to calculate the FT of the log-time sequence on a
dense frequency grid, linearly sub-sample this dense frequency grid and
then perform the inverse FT to get an approximation.
Are there any better approaches?
Bob Adams
.
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