Approximate representation of bandlimited signals
Abstract
The finite bandwidth of a communications channel imposes certain constraints upon the class of signals which may be transmitted over the channel as an acceptable level of distortion. Once these constraints are specified, there naturally, arise questions concerning the efficient representation of such signals, the maximum rate of their transmission and the possibility of signal receiver given either the time limited version of the signal or a truncated representational series. The primary focus is the approximate representation of bandlimited signals. The theoretical possibilities of approximating a bandlimited signal in order to transmit data at less than the Nyquist rate are explored. Several known results are modified and combined to form a general procedure that uses the inadequate transmission rate by taking samples of an appropriate signal approximation. Coefficients of the expansion are derived from those of the prolate function expansion and consequently, only knowledge of the signal over a finite time interval is needed.
 Publication:

Ph.D. Thesis
 Pub Date:
 December 1980
 Bibcode:
 1980PhDT.......105S
 Keywords:

 Analysis (Mathematics);
 Approximation;
 Bandwidth;
 Data Transmission;
 Frequency Ranges;
 Nyquist Frequencies;
 Radio Signals;
 Frequencies;
 Linear Receivers;
 Nyquist Diagram;
 Signal Distortion;
 Signal Reception;
 Signal Transmission;
 Communications and Radar