Re: Complex version of an impulse

Bergers wrote:
 
  ...

> We have to be careful with the terms used in describing signals. Analytic
> signals and complex (I and Q) signals are not necessarily the same. Reference
> pages 58-59 of Radar Detection by DiFranco and Rubin. DiFranco and Rubin define
> an analytic signal as y(t) = s(t) + jx(t),
> where x(t) is the Hilbert transform of the real signal s(t). The Fourier
> transform of y(t) has the properties Y(w) = 2S(w) for w>0, Y(0) = S(0), and
> Y(w) = 0 w<0. DiFranco and Rubin go on to say that under narrowband and
> bandlimited conditions, then y(t) = v(t) exp(j*2*w0*t) where v(t) = a(t)
> exp(jp(t)) and s(t) = a(t) cos(w0*t + p(t)). Note in the complex signal
> representation I = v(t) cos(w0*t) and Q = j v(t) sin(w0*t).

Right. Not every complex signal is analytic, but an analytic signal 
is necessarily complex. I didn't think it was necessary to point that 
out, but I'm glad you did.

Jerry
-- 
Besides a mathematical inclination, an exceptionally good mastery of 
one's native tongue is the most vital asset of a competent programmer.
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