I aquire typically 2D time traces which I process by a 2D Fourier transform. The aquisition is done line by line. First, I let the signal evolve for t1, then an action is performed that possibly changes its frequency and during t2 I sample the signal again in increments of dt:
| <<<----->>> | -------> start t1 A t2
Using that scheme, I correlate the frequencies during t1 with those during t2.
However, my signal typically lives near the diagonal in the 2D FFT like this:
I wonder whether the sampling could be adjusted to reduce the large areas in the 2D FFT that do not contain any information. Hopefully this would allow to reduce the aquisition time. Is there any sampling scheme, that allows to sample around the diagonal in a 2D FFT? It would kind of mean that the delta frequency between time period 1 and time period 2 are assumed to be small.