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Re: Complex version of an impulse

Started by Jerry Avins April 17, 2004
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. &#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;&#2013266095;