MothNik
commented
2 months ago I will make this consider two cases where the signal's Fourier Transform can be:
- band-limited by a low pass filter, i.e., there is a frequency $\omega_{max}$ beyond which all Fourier coefficients are 0 (given the natural band limit of the Hermite functions)
- band-limited between a lower frequency $\omega{min}$ and a high frequency $\omega{max}$. Outside of this window, all Fourier coefficients are 0 (by shifting the Hermite functions in the frequency domain and mirroring them on the y-axis)
Both scenarios could have nice applications for band-limited extrapolation.
The Hermite functions - as defined now - are defined in the frequency domain. Therefore, their Inverse Fourier Transform will be required to fit data in the time domain.