Reply by Rick Lyons 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-]
Reply by Randy Yates 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 Rick Lyons 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 glen herrmannsfeldt 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 Eric Jacobsen 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 Rick Lyons June 24, 20142014-06-24
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-]
Reply by Randy Yates June 24, 20142014-06-24
Rick Lyons <R.Lyons@_BOGUS_ieee.org> writes:

> On Wed, 18 Jun 2014 18:01:07 -0400, Randy Yates > <yates@digitalsignallabs.com> wrote: > >>Rick Lyons <R.Lyons@_BOGUS_ieee.org> writes: >> >>> On Fri, 13 Jun 2014 17:39:41 -0500, Tim Wescott >>> <tim@seemywebsite.really> wrote: >>> > [Snipped by Lyons] >>>> >>>>As mentioned, it's e^(-i*w0*t), but that's a nit -- particularly because >>>>the operation will still work (why is left as an exercise to the reader). >>> >>> Hi Tim, >>> For normal symmetrial bandpass (commercial) AM, >>> yes the e^(-i*w0*t) is a "nit". >> >>Is it? For x(t) = sin(w_c * t), one demodulation will give you x(t), the >>other will give you -x(t). Yes, that's inaudible. Is having all the >>quadrature components inaudible? I think, but I'm not sure. >> >>And who said the application here is audio? I.e., the negation may be a >>show-stopper. > > Hi Randy, > I don't understand what you have in mind here, but > I will say that my reply to Tim's post was far too > brief. What I had in mind was that with standard > broadcast AM, the RF spectrum looks like: > > > * * DSB AM * * > ** ** ** ** > * * * * * * * * > --* * * * *---//-----//---* * * * *-- > | | | > -wo 0 wo > > where 'wo' is the RF carrier freq in radians/sec.
> 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? -- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com
Reply by Andre June 23, 20142014-06-23
Dear all,

thanks for all the feedback, that was much more than expected!!!

Just to add some light on what I am doing:
I want to detect a "second source" that will add to my signal
at the same frequency, and depends on its amplitude with some
nonlinear function.

To separate the added signal from my original signal (which are
both audio signals), I thought to modulate the transmitted signal
by just a pure sine and look for overtones of this modulation
in the recorded signal.

However, it does not seem to work as easy as I thought.

best regards,

Andre



On 14.06.2014 00:39, Tim Wescott wrote:
> On Fri, 13 Jun 2014 15:26:22 +0200, Andre wrote: > >> Hi all, >> >> I am a bit stuck in a demodulation thing. >> >> Lets say I have a system that generates an AM signal and wants to detect >> distorsions of the LF signal after feeding the AM modulated signal >> through a potentially nonlinear system. >> >> This means I have phase locked TX and RX. > > How so? AM has never required phase locking -- the TX can free run, and > the RX can do envelope detection. > >> Lets say I modulate a signal at f0 with sine at f1 with 100% modulation: >> >> signal = sin(w0*t) * (0.5 + 0.5 * sin(w1*t)) >> >> I then receive this signal and downmix it by multiplying with sin and >> cos of the carrier frequency, in complex writing: >> >> baseband = received_signal * e^(i*w0*t) > > As mentioned, it's e^(-i*w0*t), but that's a nit -- particularly because > the operation will still work (why is left as an exercise to the reader). > > For that matter, if the receiver really is phase locked, then you only > need to down-convert with sin(w0*t). > >> I have then a complex baseband signal, in which I expect sidebands at +- >> f1. > > Again, as mentioned, you're neglecting the signal at 2*f0 here, which one > would usually filter out. > >> Lets say I am after the overtones of that f1 in the complex baseband >> signal. For example, I want to detect components at +-f2 with f2 = 2*f1. >> >> Can I not just multiply the complex baseband signal with e^(i*w2*t) to >> get the (compelex)component at f2? >> Like: >> >> what_i_look_for = baseband * e^(i*w2*t) > > You could, yes. That'll only yet you the second harmonic of the > fundamental, though -- it'll miss the third, fourth, etc. > >> Or do I miss some conjugate etc? >> >> As said above, everything is phase locked, so I do not need to recover >> any phase. > > I don't know if your "everything is phase locked" statement comes from > naivet&eacute; or from some system feature you're not sharing with us, but in > conventional AM reception you _do_ need to recover phase, usually via a > PLL, or you do envelope detection and stay blithely unaware of phase. >
Reply by Bob Masta June 22, 20142014-06-22
On Sun, 22 Jun 2014 00:21:59 -0400, robert bristow-johnson
<rbj@audioimagination.com> wrote:

>On 6/21/14 11:45 PM, Rick Lyons wrote: >> On Fri, 13 Jun 2014 14:22:19 -0400, robert bristow-johnson >> <rbj@audioimagination.com> wrote: >> >>> On 6/13/14 9:26 AM, Andre wrote: >>>> Hi all, >>>> >>>> I am a bit stuck in a demodulation thing. >>>> >>>> Lets say I have a system that generates an AM signal and >>>> wants to detect distorsions of the LF signal after feeding >>>> the AM modulated signal through a potentially nonlinear system. >>>> >>>> This means I have phase locked TX and RX. >>> >>> well, we normally get phase locking between TX and RX because the >>> carrier is not suppressed. commercial AM that is not over-modulated is >>> not quite the same thing as DSB-SC. it is because of this that one can >>> use a simple rectifier (like the 1N34 i used in a crystal radio 5 >>> decades ago - sheeesh i'm getting old!) to demodulate the AM. >> >> [Snipped by Lyons] >> >> Hi Robert, >> I was always under the impression that standard >> commercial broadcast AM transmitted energy at the >> carrier frequency (therefore it is not DSB-SC). >> >> Is that true? (I did a little searching on the >> web to answer my "Is that true?" question but >> I failed to find an answer.) > >it has to be true. i know so, simply from my ham radio days. how else >does 100% modulation or "overmodulation" have meaning? how could a >rectifier work for demodulation.
Definitely true. This is normal AM, where the instantaneous value of the signal modulates the amplitude of the carrier. Witn no signal, the carrier is at 50% amplitude. Positive signal increases the carrier amplitude, and negative decreases it. As you note, if the signal goes too far negative it "breaks through" into overmodulation. (And in the real world, if it goes to far positive it can clip in the RF amps and transmitter.) The simplest way to get supressed carrier is to use a conventional 4-quadrant multiplier in place of the AM (which is a biased 2-quadrant multiplier). Then you have the sum-and-difference components (only!) that we first saw in high-school trig formulas for the product of sinusoids. The classical formula for AM is: sin(carrier) * [1 + Depth * sin(modulator)] But for signal generator applications (not broadcast radio) I prefer: sin (carrier) * [1 - Depth/2 + Depth/2 * sin(modulator)] This makes more intuitive sense (to me, anyway), and is more practical to use. At Depth=0 you get only the carrier, at 100% amplitude. As you increase Depth, the peaks of the modulated waveform still go to 100%, with troughs down to 50%. At 100% Depth the peaks are still the same, with the troughs at 0. So you are always using the full-scale range of your D/A (or transmitter) for maximum dynamic range. As a nice little side benefit, 200% Depth converts this into a simple multiplier for suppressed carrier. <http://www.daqarta.com/dw_aa0d.htm> Best regards, Bob Masta DAQARTA v7.60 Data AcQuisition And Real-Time Analysis www.daqarta.com Scope, Spectrum, Spectrogram, Sound Level Meter Frequency Counter, Pitch Track, Pitch-to-MIDI FREE Signal Generator, DaqMusiq generator Science with your sound card!
Reply by Randy Yates June 22, 20142014-06-22
Rick Lyons <R.Lyons@_BOGUS_ieee.org> writes:

> On Wed, 18 Jun 2014 18:01:07 -0400, Randy Yates > <yates@digitalsignallabs.com> wrote: > >>Rick Lyons <R.Lyons@_BOGUS_ieee.org> writes: >> >>> On Fri, 13 Jun 2014 17:39:41 -0500, Tim Wescott >>> <tim@seemywebsite.really> wrote: >>> > [Snipped by Lyons] >>>> >>>>As mentioned, it's e^(-i*w0*t), but that's a nit -- particularly because >>>>the operation will still work (why is left as an exercise to the reader). >>> >>> Hi Tim, >>> For normal symmetrial bandpass (commercial) AM, >>> yes the e^(-i*w0*t) is a "nit". >> >>Is it? For x(t) = sin(w_c * t), one demodulation will give you x(t), the >>other will give you -x(t). Yes, that's inaudible. Is having all the >>quadrature components inaudible? I think, but I'm not sure. >> >>And who said the application here is audio? I.e., the negation may be a >>show-stopper. > > Hi Randy, > I don't understand what you have in mind here, but > I will say that my reply to Tim's post was far too > brief. What I had in mind was that with standard > broadcast AM, the RF spectrum looks like: > > > * * DSB AM * * > ** ** ** ** > * * * * * * * * > --* * * * *---//-----//---* * * * *-- > | | | > -wo 0 wo > > where 'wo' is the RF carrier freq in radians/sec. > 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).
Hi Rick, I presume what you are representing above in the "ascii spectrum" (pretty nice, BTW!) is the magnitude of the original baseband spectrum, shifted up and down by wo. Right? I agree that this is what the spectrum magnitude looks like. However, plotting just the magnitude obscures the detail that is behind my point. Separate out from the magnitude the real and imaginary components and let's discuss those. 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. 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. That's why I said sin(wt) would change into -sin(wt), since sin has imaginary spectral components. Shew! That was tought to explain. Did you get it? --Randy
> > But for single sideband AM the RF spectrum looks > like: > > * SSB AM * > ** ** > * * * * > --* *------//-----//------* *-- > | | | > -wo 0 wo > > In this SSB case, complex down-conversion > [e^(-i*w0*t)] will produce a different result > than complex up-conversion [e^(i*w0*t)]. > That's what I was thinking. > > Hey, wait a minute! Why are we using 'i' > instead of 'j' in these complex-valued > expressions? I can show you in the Bible > where God wants us to use 'j', and not 'i'. > Anyone who uses 'i' will surely end up in > the place of eternal damnation. > > [-Rick-]
-- Randy Yates Digital Signal Labs http://www.digitalsignallabs.com