Signal representation by instantaneous amplitude and phase
Abstract
The conditions under which the phase and amplitude of a signal can be obtained through canonical calculations are examined analytically. It is shown that a spectral examination of signal, assuming that the amplitude is held constant, will yield a canonical form for the phase. It is further demonstrated that under deterministic conditions there will be a unique spectral line associated with the amplitude and phase couple, with the spectral continuum continuing upward from that point. For random signals, however, a Hilbert transformation of the couple reveals that the statistical link between the instantaneous amplitude and phase ceases to be valid in canonical form.
- Publication:
-
Annals of Telecommunications
- Pub Date:
- June 1983
- Bibcode:
- 1983AnTel..38..179P
- Keywords:
-
- Amplitudes;
- Canonical Forms;
- Communication Theory;
- Complex Variables;
- Phase Modulation;
- Signal Analysis;
- Fourier Transformation;
- Hilbert Transformation;
- Random Signals;
- Communications and Radar