>Subject: Re: Complex version of an impulse >From: Jerry Avins jya@ieee.org >Date: 4/16/2004 11:46 AM Eastern Daylight Time >Message-id: <407fffe8$0$16464$61fed72c@news.rcn.com> > >robert bristow-johnson wrote: > >> In article da4d20d8.0404152109.7ed6b813@posting.google.com, Impulse at >> impulse@e.coolworks.com wrote on 04/16/2004 01:09: >> >> >>>Hi all, >>> >>>I've got an analyic signal for which I'm designing an IIR >>>filter with purely real valued coefficients. I'd like to >>>look at the impulse response of this filter, but since the >>>normal impulse is purely real and the coefficients are all >>>real, the impulse response is also purely real. >>> >>>In order to get a complex impulse response, I need a >>>complex impulse. Is this: >>> >>>.... 0 0 0 0 0 (1+i) 0 0 0 0 0 0 .... >>> >>>the right answer? >> >> >> >> there is a paper called "the Analytical Impulse" by Andrew Duncan in the >AES >> Journal that might suggest: >> >> x[n] = d[n] + j*Hilbert{ d[n] } ("d[n]" is the discrete >impulse) >> >> as the thing to bang a complex linear system with. >> >> i dunno. >> >> r b-j > >I don't get it. In the real world, an analytic signal has two parts, I >and Q, that exist on two wires. To filter an analytic signal, the parts >must be filtered separately. Inside a computer -- or our heads -- there >is more flexibility, up to a point. The samples of an analytic signal >may be thought of as pairs of samples (labeled I and Q, e.g.) or as >complex numbers with real or imaginary parts. Either way, the parts can >be filtered as separate streams. It seems to me that without great >cleverness, they have to be. > >Jerry >-- >Engineering is the art of making what you want from things you can get. >����������������������������������������������������������������������� > > > > > > >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). Scott

# Re: Complex version of an impulse

Started by ●April 16, 2004