Integral representations and sampling theorems of periodic functions and their Hilbert transforms
Abstract
Integral representations are given for periodic functions resulting from their Fourier series, and these are used to produce integral representations for their Hilbert transforms. Sampling theorems are acquired for the functions themselves as well as for their Hilbert transforms by limiting to band-limited periodic functions.
- Publication:
-
NASA STI/Recon Technical Report N
- Pub Date:
- September 1973
- Bibcode:
- 1973STIN...7624439K
- Keywords:
-
- Hilbert Transformation;
- Periodic Functions;
- Sampling;
- Theorems;
- Bandpass Filters;
- Fourier Series;
- Integral Equations;
- Signal Processing;
- Transfer Functions;
- Communications and Radar