DUALITY AND INFORMATION COMPONENTS IN FOURIER TRANSFORMS.

This paper considers signals or waveshapes in terms of their information components and considers the dual representation of signals in Fourier transform domains. Certain duality aspects between Fourier series and sampling theorem expansions are discussed. The duality between linear transmission and analytic signal modulation is pointed out, of which, the duality between distortions echoes in the time domain and sidebands in the frequency domain is a particular example. It is shown that sampling theorem expansions can be expressed in terms of distortion echoes of the elementary function delta t-t and also in terms of sidebands of the elementary function e j2 pi ft. Relations between waveshape properties in the time and frequency domains are considered from several points-of-view and new insight is thereby gained. The relation between the autocorrelation function and intersymbol influence is analyzed, and the importance of phase distortion echoes, previously ignored in this connection, is pointed out. Finally, there is a discussion of the relations between signal structure and resolution. In the appendices, certain characteristics of analytic signals and Hilbert transforms which are of interest in modulation theory are derived. Some of these the writer has not been able to find in previous literature. Author