Representation of signals
Abstract
The representation of deterministic signals is dealt with starting from the signal space considered as a vectorial space. Various representations are discussed including discretization through orthogonal complete bases and continuous representations with emphasis on the Fourier transform. For random signals the linear filtering is detailed, and the KarhunenLoeve expansion is discussed. The fundamental functionals related to representation of signals in the conjugate spaces of time and frequency are discussed with regard to the product of useful duration times useful bandwidth, degrees of freedom of a slice of duration T for a band limited signal, and the ambiguity function of the signal.
 Publication:

NASA STI/Recon Technical Report N
 Pub Date:
 October 1975
 Bibcode:
 1975STIN...7710409J
 Keywords:

 Communication Theory;
 Representations;
 Signal Analysis;
 Autocorrelation;
 Fourier Transformation;
 Integral Equations;
 KarhunenLoeve Expansion;
 Linear Filters;
 Power Spectra;
 Random Processes;
 Vector Spaces;
 Communications and Radar