Bounds, sampling, and amplitude uncertainty of band-limited functions
Abstract
A comprehensive analysis of the average rate of change of band limited functions is presented, including a derivation of the least upper bound on functions for which either the zeroth absolute moments (spectral areas) or Fourier amplitude spectra of the functions are bounded. These results are extended to the case of functions that are limited in both frequency and amplitude. The average rate of change of a function over an interval in which one end point of the interval is an extremum of the function is similarly bounded and used to establish a sampling rate which guarantees that, between successive samples of a band limited function, the function itself does not deviate from either sample by more than predefined amplitude change. Based on these results, several problems of practical importance, including slope overload error in delta modulation, aperture time and amplitude uncertainty in analog to digital conversion, the estimation of level crossing statistics, and the detection and elimination of high frequency pulses from a low frequency signal, are examined.
- Publication:
-
Ph.D. Thesis
- Pub Date:
- 1980
- Bibcode:
- 1980PhDT........51W
- Keywords:
-
- Digital Data;
- Frequency Modulation;
- Signal Processing;
- Analog To Digital Converters;
- Delta Modulation;
- Discrete Functions;
- Communications and Radar