I have problems with figuring out how to FFT TPPI-acquired data. I try to do
it myself (without the spectrometer software) on simulated data.
I have some conceptual difficulty understanding what kind of FFT I should use.
My simulated data (1D) is:
fid(t)=[exp(-i*t*omega)+exp(i*t*omega)]*exp(-t/T2)
where the 1st term in is I+ coherence and the second I- (or the other way
round). The fid is now amplitude modulated, the imaginary parts cancel.
When I do a complex (ordinary) FFT I get 2 peaks, one at +omega and one at
-omega corresponding to the 2 coherences.
Using TPPI (increment the pulse phase before evolution by 90 deg. wrt the
previous point) I have to phase shift the I- coherence by -90 and the I+
coherence by +90 (or the other way round). In this way the 2 peaks are moved
by f(Nyquist)/2 to the left and right, respectively. This I can observe by
complex FFT again.
The books say that I have to use a *real* FFT to get the 2 coherences folded
onto each other in a way that only absorptive signals remain. But when I use a
*real* FFT (which is a cosine transform in my interpretation) I get the same
pattern, i.e. 2 peaks. (the same happens when I use a sine transform).
Which FFT should I use, or where did I make an error ?
Thank you
Alexej Jerschow
PS: I encountered the same problem when trying to simulate the States method:
Every other point shifted by 90 deg (the pulse phase), then combine two points
as real and imaginary parts. Complex FFT should yield the desired result but
it did not in my case.