LT Spice FFT scaling

You compute the coordinate of the point on the new uniform grid and take the integer part, then you use the remainder to look up into a prepared table of the interpolation function which by smearing the wanted frequency across a series of nearby bins makes a very good approximation to the right frequency multiplied by a smooth frequency dependent fiddle factor in the frequency domain. It is a variant of:

sin(Nx) + sin((N+1)x) = 2sin((N+1/2)x)cos(x/2)

But obviously in practice taking a few more terms and other weights.

Usually done over an odd numbered region of support typically 7 or 9 and capable of removing aliases and delivering DFT quality results from FFT. There is a more sophisticated version that came later and deliberately throws away results too close to the edge of the transform to get the very best possible accuracy on the part that is being kept. It is routine in almost all indirect FFT based imaging these days.

IOW you interpolate on the convolving function to match what you want by way of frequency. A bit of normalisation to sort out the sampling non-uniformities and you are done.

The devil *is* in the detail. Any kind of error in the implementation and you can end up with truly horrible artefacts.

It is something that really only interests very serious FFT geeks mostly in radio astronomy but also MRI and SAR. You can get away with cruder methods but to get ultimate dynamic range then you have to use all the right tricks.

Provided that the waveform matched periodic boundary conditions exactly applying a windowing function merely broadens the peak. The idea of windowing is to avoid a discontinuity across the wrap around of data.

FFTs are so efficient at generating reasonable-looking wrong answers that techniques to prevent that are super useful.

Cheers

Phil Hobbs