On Tue, 24 Jun 2014 00:22:22 -0400, Randy Yates <yates@digitalsignallabs.com> wrote: [Snipped by Lyons]> > >> SO. ...COMPLEX DOWN-CONVERSION [E^(-I*W0*T)] OR >> COMPLEX UP-CONVERSION [E^(I*W0*T)] WILL BOTH >> TRANSLATE THE RF SIGNAL (WITH SYMMETRICAL SIDEBANDS) >> TO BE CENTERED AT 0 RAD/SEC (0 HZ). > >(emphasis mine) > >Rick, let me be a little more critical. Yes, both will "translate" the >RF signal to be centered at 0 rad/sec, but you do NOT get exactly the >same thing at baseband in each case. > >Do you agree?Hi Randy, I believe complex down-conversion followed by lowpass filtering will produce the exact same complex baseband (centered at 0 Hz) signal as complex up-conversion followed by lowpass filtering. Randy, I'll send you a private e-mail with an MS Word document containing figures to validate what I'm saying. If I'm "all mixed up" here I trust you'll straighten me out. Regards, [-Rick-]
Question on AM demodulation...
Started by ●June 13, 2014
Reply by ●June 24, 20142014-06-24
Reply by ●June 24, 20142014-06-24
On Tue, 24 Jun 2014 04:11:48 -0700, Rick Lyons <R.Lyons@_BOGUS_ieee.org> wrote:>On Tue, 24 Jun 2014 00:22:22 -0400, Randy Yates ><yates@digitalsignallabs.com> wrote: > > [Snipped by Lyons] >> >> >>> SO. ...COMPLEX DOWN-CONVERSION [E^(-I*W0*T)] OR >>> COMPLEX UP-CONVERSION [E^(I*W0*T)] WILL BOTH >>> TRANSLATE THE RF SIGNAL (WITH SYMMETRICAL SIDEBANDS) >>> TO BE CENTERED AT 0 RAD/SEC (0 HZ). >> >>(emphasis mine) >> >>Rick, let me be a little more critical. Yes, both will "translate" the >>RF signal to be centered at 0 rad/sec, but you do NOT get exactly the >>same thing at baseband in each case. >> >>Do you agree? > >Hi Randy, > I believe complex down-conversion followed by lowpass >filtering will produce the exact same complex baseband >(centered at 0 Hz) signal as complex up-conversion followed >by lowpass filtering. > >Randy, I'll send you a private e-mail with an MS Word >document containing figures to validate what I'm >saying. If I'm "all mixed up" here I trust >you'll straighten me out. > >Regards, >[-Rick-]This is true for some cases, but, importantly, not all. It is true for two cases: If the signal spectrum is symmetric about the center of the bandwidth (e.g., DSB) and it is mixed to baseband so that the center of symmetry is at DC, then the sign of the mixer frequency doesn't matter. If the signal spectrum is asymmetric but mixed down so that the signal spectrum is contained between 0 Hz and the signal BW, it's image will still be reflected from 0 Hz to -BW and the sign of the mixer frequency doesn't matter. A practical example of this technique would be demodulation of a vestigial sideband signal. It is NOT true if the signal spectrum is asymmetric and it is mixed to baseband so that the center of the signal BW is at 0 Hz. In this case the signal spectrum will be inverted (i.e., reversed) or not depending on the sign of the mixing frequency. In many systems selection of spectral inversion is done by changing the sign of the mixing frequency, in both modulator and demodulator. Eric Jacobsen Anchor Hill Communications http://www.anchorhill.com
Reply by ●June 24, 20142014-06-24
Eric Jacobsen <eric.jacobsen@ieee.org> wrote:> On Tue, 24 Jun 2014 04:11:48 -0700, Rick Lyons(snip)>> I believe complex down-conversion followed by lowpass >>filtering will produce the exact same complex baseband >>(centered at 0 Hz) signal as complex up-conversion followed >>by lowpass filtering.(snip)> This is true for some cases, but, importantly, not all.> It is true for two cases:(snip of two cases)> It is NOT true if the signal spectrum is asymmetric and it is mixed to > baseband so that the center of the signal BW is at 0 Hz. In this > case the signal spectrum will be inverted (i.e., reversed) or not > depending on the sign of the mixing frequency.> In many systems selection of spectral inversion is done by changing > the sign of the mixing frequency, in both modulator and demodulator.I think this is a lost art. In the days before all TV sets were required to have UHF tuners, there were UHF converter boxes. I believe a single conversion down to VHF channel 3 or 4, and appropriate filtering. Then there were cable boxes that converted cable channels down to low VHF channels, which I believe had to do two conversions. The lower cable channels overlap the low VHF channels, so they mix up to some higher frequency, and then back down to the appropriate output frequency. (Or down to baseband, but, as well as I remember, they didn't do that.) In this case, you could do two inversions, or zero, and still get the right output. Then there was MDS, a microwave (about 2.3GHz) system that was sometimes used for early broadcast pay-TV systems. As well as I remember it, the broadcast signal is inverted from the usual VSB, such that the converter has to invert it. -- glen
Reply by ●June 24, 20142014-06-24
On Tue, 24 Jun 2014 15:23:28 GMT, eric.jacobsen@ieee.org (Eric Jacobsen) wrote:>On Tue, 24 Jun 2014 04:11:48 -0700, Rick Lyons ><R.Lyons@_BOGUS_ieee.org> wrote:[Snipped by Lyons]>> >>Hi Randy, >> I believe complex down-conversion followed by lowpass >>filtering will produce the exact same complex baseband >>(centered at 0 Hz) signal as complex up-conversion followed >>by lowpass filtering. >> >>Randy, I'll send you a private e-mail with an MS Word >>document containing figures to validate what I'm >>saying. If I'm "all mixed up" here I trust >>you'll straighten me out. >> >>Regards, >>[-Rick-]Hi Eric,>This is true for some cases, but, importantly, not all. > >It is true for two cases: > >If the signal spectrum is symmetric about the center of the bandwidth >(e.g., DSB) and it is mixed to baseband so that the center of symmetry >is at DC, then the sign of the mixer frequency doesn't matter.Yep, that was the case I was considering. A real-valued DSB AM signal that had spectral magnitude symmetry centered at the positive carrier freq and centered at the negative carrier freq. I interpret your word "mixed" to mean complex down-conversion or complex up conversion. [Snipped by Lyons-] [-Rick-]
Reply by ●July 3, 20142014-07-03
Folks, I was wrong about this. It doesn't matter whether you shift the negative or the positive to DC (as most of you probably already knew). I got hung up "in my head" without writing stuff out. Ouch! Further, I didn't find my error on my own - Rick had to point it out to me with a diagram he shared in a private email. And now, the painful crow-eating: Randy Yates <yates@digitalsignallabs.com> writes:> [...] > If we assume we have a real baseband signal r(t), then R(w) = R*(-w), > which is that so-called Hermitian symmetry. (I love that term, don't > you?) That means that Re(R(w)) = Re(R(-w)) and Im(R(w)) = -Im(R(-w)); > > In other words, the negative and positive components of the real part of > the spectrum of the baseband components can be swapped without changing > anything. However, if you swapped the negative and positive components > of the imaginary part of the spectrum of the baseband components, you > would NOT have the exact same thing; you would have Im(R(w)) = -1 * > Im(W(w)), where W(w) is the spectrum of a signal that is identical to > R(w) except that the positive and negative components of the imaginary > part of the signal have been swapped.So far this is correct.> And that is precisely the difference between shift the negative > component of BANDPASS signal to DC versus shifting the positive > component of the BANDPASS signal to DC - the real parts of the spectrum > of those two results are identical, but the imaginary parts are > negatives of one another.This is my error. They are not the negative of one another. You end up with the exact same imaginary spectrum. If you think it through, you'll see that the odd-symmetric spectrum of the original baseband signal is shifted both up and down to fc (carrier) on modulation, and so both have the same relationship (odd-symmetric) about the carrier. Sorry if I caused any confusion. -- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com
Reply by ●July 4, 20142014-07-04
On Thu, 03 Jul 2014 15:43:56 -0400, Randy Yates <yates@digitalsignallabs.com> wrote:>Folks, > >I was wrong about this. It doesn't matter whether you shift the negative >or the positive to DC (as most of you probably already knew). I got hung >up "in my head" without writing stuff out. Ouch! > >Further, I didn't find my error on my own - Rick had to point it out to >me with a diagram he shared in a private email. > >And now, the painful crow-eating:Hi Randy, Your error was NOT nearly as significant as you're making out here. Your mistake was in answering a "thought problem", and a common mistake it is. I've made the exact same mistake myself. Ha ha Randy. I've made mistakes FAR more significant than your little one here. Being able to admit a mistake (however small that mistake is) is a sign of a strong character. "Admitting error clears the Score, and proves you wiser than before." -Arthur Guiterman [-Rick-]
