nick@paladin.owego.ny.us (Carmine Nicoletta) (03/02/91)
What's an analytic signal?
jroth@allvax.enet.dec.com (Jim Roth) (03/05/91)
In article <667888143.106091@paladin.owego.ny.us>, nick@paladin.owego.ny.us (Carmine Nicoletta) writes... >What's an analytic signal? If your real signal is x(t), then the "analytic signal" is x(t) + j y(t), where y(t) is the Hilbert transform of x(t) and j is sqrt(-1) [I demonstrate that I'm an electrical engineer with this notation.] The Hilbert transform of a signal takes all sinusoidal components of its Fourier spectrum and phase shifts them by 90 degrees. In a sense you can identify the real signal x(t) with the potential energy of a signal and the imaginary y(t) with the kinetic energy; thus the magnitude of the analytic signal represents the total energy. Consider a simple resonant circuit ringing down after an impulse - the voltage across the capacitor may be x(t) representing potential or electrostatic energy while the current in the inductor y(t) represents the kinetic energy of the magnetic field. Think also of the idea of "rotating phasors"... See texts such as Papoulis or Bracewell on Fourier integrals for a more detailed description. - Jim