What makes quadrature mixing possible?

On 09/01/2014 07:57 AM, Tim Wescott wrote:
> On Sun, 31 Aug 2014 21:48:47 +0000, glen herrmannsfeldt wrote:
>
>> miladsp <99479@dsprelated> wrote:
>>
>>> so I've been reading quadrature signals, quadrature mixing and hilbert
>>> transform and while most of it makes sense I find quadrature mixing a
>>> bit confusing. What I can't get my head around is the fact that we can
>>> transmit in-phase and quadrature parts of the signal on the same
>>> physical channel. What are exploiting here? Am I right in thinking that
>>> we're essentially transmitting a complex signal using a real signal?
>>
>> The chrominance subcarrier in an NTSC video signal is an interesting
>> example.
>
> An old TV engineer of my acquaintance called NTSC "Never The Same Color".
> I think he had one for PAL, too.
>
Pale And Lurid was the usual one for PAL.

Steve

On Sun, 31 Aug 2014 17:33:39 -0500, "miladsp" <99479@dsprelated>
wrote:

>By the way, almost all articles on the subject have references to "Complex
>Signals" series by "N. Boutin" in "RF Design" but I can't find any links to
>them. Does any one know where they can be found?	 

Hello miladsp,
   I couldn't find an electronic copy of 
Noel Boutin's "Complex Signals" article 
on the web.  (Actually, it was a series of 
four articles.)  That's too bad.

It appears that Prof. Boutin is still with the 
University of Sherbrooke in Quebec.

You might send him an e-mail and very respectfully 
ask if he is willing to send you an electronic copy 
of his four-part article.  (If you are successful
miladsp, PLEASE LET US KNOW, OK?)

See:

http://www.usherbrooke.ca/ssf/documentation/grandes-entrevues/noel-boutin/


Good Luck,
[-Rick-]

>> I find quadrature mixing a bit confusing.

Hi,

maybe things clear up a bit if you consider that the real part represents
the sine component of the radio frequency signal and the imaginary part the
cosine component. The two are orthogonal.

As a practical example: I've got a box labeled "Agilent MXG" on my desk
that has two coax cable inputs for I and Q and a button to set the carrier
frequency. Connect a voltage to either input and it will control (modulate)
the respective component that you get at the coax cable output. Simple as
that.

"Hilbert" gets more complicated as now you are dealing with a device that
turns a sine wave into a cosine wave. The task is sort of impossible (what
is it supposed to do with a constant input voltage?) but approximations
exist. 
Still, Hilbert transform is not necessary for quadrature processing /
direct conversion mixing.	 

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On Sunday, August 31, 2014 8:23:30 PM UTC-5, Steve Underwood wrote:
> On 09/01/2014 07:57 AM, Tim Wescott wrote:
> 
> > On Sun, 31 Aug 2014 21:48:47 +0000, glen herrmannsfeldt wrote:
> 
> >
> 
> >> miladsp <99479@dsprelated> wrote:
> 
> >>
> 
> >>> so I've been reading quadrature signals, quadrature mixing and hilbert
> 
> >>> transform and while most of it makes sense I find quadrature mixing a
> 
> >>> bit confusing. What I can't get my head around is the fact that we can
> 
> >>> transmit in-phase and quadrature parts of the signal on the same
> 
> >>> physical channel. What are exploiting here? Am I right in thinking that
> 
> >>> we're essentially transmitting a complex signal using a real signal?
> 
> >>
> 
> >> The chrominance subcarrier in an NTSC video signal is an interesting
> 
> >> example.
> 
> >
> 
> > An old TV engineer of my acquaintance called NTSC "Never The Same Color".
> 
> > I think he had one for PAL, too.
> 
> >
> 
> Pale And Lurid was the usual one for PAL.
> 
> 
> 
> Steve

And SECAM (the French standard which was
incompatible with everything else) stood for
System Essentially Contrary to American Method.

>On Sun, 31 Aug 2014 17:33:39 -0500, "miladsp" <99479@dsprelated>
>wrote:
>
>>By the way, almost all articles on the subject have references to
"Complex
>>Signals" series by "N. Boutin" in "RF Design" but I can't find any links
to
>>them. Does any one know where they can be found?	 
>
>Hello miladsp,
>   I couldn't find an electronic copy of 
>Noel Boutin's "Complex Signals" article 
>on the web.  (Actually, it was a series of 
>four articles.)  That's too bad.
>
>It appears that Prof. Boutin is still with the 
>University of Sherbrooke in Quebec.
>
>You might send him an e-mail and very respectfully 
>ask if he is willing to send you an electronic copy 
>of his four-part article.  (If you are successful
>miladsp, PLEASE LET US KNOW, OK?)
>
>See:
>
>http://www.usherbrooke.ca/ssf/documentation/grandes-entrevues/noel-boutin/
>
>
>Good Luck,
>[-Rick-]
>

Hi Rick! I'm waiting for a reply from him. I'll let you guys know if I get
a copy.

Now some further questions about quadrature modulation. First let's assume
our physical channel consists of two coax cables (just like the example in
your book) which means we can physically transmit complex signals. Now, am
I right in thinking that two complex signals (e^jwt) and (e^jwt+pi/2) are
orthogonal?? If they are, can we use them as carriers for transmitting two
independent signals??

The reason I'm asking is that I'm trying to follow quadrature modulation in
frequency domain, and I can see how in-phase or quadrature parts cancel
each other out and it's all fine, but shouldn't I be able to see
orthogonality if I just look at one side (positive or negative) of the
frequency domain? Is the negative frequency content just there to make the
signal real or it's what actually makes quadrature modulation possible?

To be honest, I didn't quite understand what I wrote, I hope you guys do!	


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On Tue, 02 Sep 2014 15:02:59 -0500, miladsp wrote:

>>On Sun, 31 Aug 2014 17:33:39 -0500, "miladsp" <99479@dsprelated>
>>wrote:
>>
>>>By the way, almost all articles on the subject have references to
> "Complex
>>>Signals" series by "N. Boutin" in "RF Design" but I can't find any
>>>links
> to
>>>them. Does any one know where they can be found?
>>
>>Hello miladsp,
>>   I couldn't find an electronic copy of
>>Noel Boutin's "Complex Signals" article on the web.  (Actually, it was a
>>series of four articles.)  That's too bad.
>>
>>It appears that Prof. Boutin is still with the University of Sherbrooke
>>in Quebec.
>>
>>You might send him an e-mail and very respectfully ask if he is willing
>>to send you an electronic copy of his four-part article.  (If you are
>>successful miladsp, PLEASE LET US KNOW, OK?)
>>
>>See:
>>
>>http://www.usherbrooke.ca/ssf/documentation/grandes-entrevues/noel-
boutin/
>>
>>
>>Good Luck,
>>[-Rick-]
>>
>>
> Hi Rick! I'm waiting for a reply from him. I'll let you guys know if I
> get a copy.
> 
> Now some further questions about quadrature modulation. First let's
> assume our physical channel consists of two coax cables (just like the
> example in your book) which means we can physically transmit complex
> signals. Now, am I right in thinking that two complex signals (e^jwt)
> and (e^jwt+pi/2) are orthogonal?? If they are, can we use them as
> carriers for transmitting two independent signals??
> 
> The reason I'm asking is that I'm trying to follow quadrature modulation
> in frequency domain, and I can see how in-phase or quadrature parts
> cancel each other out and it's all fine, but shouldn't I be able to see
> orthogonality if I just look at one side (positive or negative) of the
> frequency domain?

I'm almost certain the answer is no.  The orthogonality is a time-domain 
thing that does not translate well to the frequency domain.

> Is the negative frequency content just there to make
> the signal real or it's what actually makes quadrature modulation
> possible?

If you're talking about the reflection of the RF signal, it's not there to 
_make_ the signal real, it's there as a _consequence_ of the _fact_ that 
the signal is real.

But it doesn't need to be there to make quadrature modulation possible, 
and you can do all your math without paying attention to the negative part 
of the RF signal -- because the RF signal _is_ real, it's negative part is 
completely a function of its positive part.

-- 

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

>On Tue, 02 Sep 2014 15:02:59 -0500, miladsp wrote:
>
>>>On Sun, 31 Aug 2014 17:33:39 -0500, "miladsp" <99479@dsprelated>
>>>wrote:
>>>
>>>>By the way, almost all articles on the subject have references to
>> "Complex
>>>>Signals" series by "N. Boutin" in "RF Design" but I can't find any
>>>>links
>> to
>>>>them. Does any one know where they can be found?
>>>
>>>Hello miladsp,
>>>   I couldn't find an electronic copy of
>>>Noel Boutin's "Complex Signals" article on the web.  (Actually, it was
a
>>>series of four articles.)  That's too bad.
>>>
>>>It appears that Prof. Boutin is still with the University of Sherbrooke
>>>in Quebec.
>>>
>>>You might send him an e-mail and very respectfully ask if he is willing
>>>to send you an electronic copy of his four-part article.  (If you are
>>>successful miladsp, PLEASE LET US KNOW, OK?)
>>>
>>>See:
>>>
>>>http://www.usherbrooke.ca/ssf/documentation/grandes-entrevues/noel-
>boutin/
>>>
>>>
>>>Good Luck,
>>>[-Rick-]
>>>
>>>
>> Hi Rick! I'm waiting for a reply from him. I'll let you guys know if I
>> get a copy.
>> 
>> Now some further questions about quadrature modulation. First let's
>> assume our physical channel consists of two coax cables (just like the
>> example in your book) which means we can physically transmit complex
>> signals. Now, am I right in thinking that two complex signals (e^jwt)
>> and (e^jwt+pi/2) are orthogonal?? If they are, can we use them as
>> carriers for transmitting two independent signals??
>> 
>> The reason I'm asking is that I'm trying to follow quadrature
modulation
>> in frequency domain, and I can see how in-phase or quadrature parts
>> cancel each other out and it's all fine, but shouldn't I be able to see
>> orthogonality if I just look at one side (positive or negative) of the
>> frequency domain?
>
>I'm almost certain the answer is no.  The orthogonality is a time-domain 
>thing that does not translate well to the frequency domain.
>
>> Is the negative frequency content just there to make
>> the signal real or it's what actually makes quadrature modulation
>> possible?
>
>If you're talking about the reflection of the RF signal, it's not there to

>_make_ the signal real, it's there as a _consequence_ of the _fact_ that 
>the signal is real.
>
Agreed. That's what I really meant.

>But it doesn't need to be there to make quadrature modulation possible, 
>and you can do all your math without paying attention to the negative part

>of the RF signal -- because the RF signal _is_ real, it's negative part is

>completely a function of its positive part.
>

That's exactly what I am trying to do but when I ignore the negative
frequency and just look at positive side, I can't separate the two
messages. I must be missing something obvious.

>-- 
>
>Tim Wescott
>Wescott Design Services
>http://www.wescottdesign.com
>
	 

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On Tue, 02 Sep 2014 15:02:59 -0500, "miladsp" <99479@dsprelated>
wrote:

  [Snipped by Lyons]

Hello miladsp,

>Hi Rick! I'm waiting for a reply from him. I'll let you guys know if I get
>a copy.

Great.  If you're able to obtain an electronic 
copy of Boutin's articles, it would be useful 
to many people.  I hope Prof. Boutin is 
generaous and you are successful.

>Now some further questions about quadrature modulation. First let's assume
>our physical channel consists of two coax cables (just like the example in
>your book) which means we can physically transmit complex signals. Now, am
>I right in thinking that two complex signals (e^jwt) and (e^jwt+pi/2) are
>orthogonal?? If they are, can we use them as carriers for transmitting two
>independent signals??

I forget what is the formal definition of 
orthogonality.  I think it has to do with 
the integral of the product of two signals 
being equal to zero.  Something like that.

>The reason I'm asking is that I'm trying to follow quadrature modulation in
>frequency domain, and I can see how in-phase or quadrature parts cancel
>each other out and it's all fine, but shouldn't I be able to see
>orthogonality if I just look at one side (positive or negative) of the
>frequency domain? Is the negative frequency content just there to make the
>signal real or it's what actually makes quadrature modulation possible?

I'm not exactly sure what you're asking here.
Can you ask your questions by relating them 
to specific figures in my book or specific 
figures in my online qudrature tutorial article?

[-Rick-]

>On Tue, 02 Sep 2014 15:02:59 -0500, "miladsp" <99479@dsprelated>
>wrote:
>
>  [Snipped by Lyons]
>
>Hello miladsp,
>
>>Hi Rick! I'm waiting for a reply from him. I'll let you guys know if I
get
>>a copy.
>
>Great.  If you're able to obtain an electronic 
>copy of Boutin's articles, it would be useful 
>to many people.  I hope Prof. Boutin is 
>generaous and you are successful.
>
>>Now some further questions about quadrature modulation. First let's
assume
>>our physical channel consists of two coax cables (just like the example
in
>>your book) which means we can physically transmit complex signals. Now,
am
>>I right in thinking that two complex signals (e^jwt) and (e^jwt+pi/2)
are
>>orthogonal?? If they are, can we use them as carriers for transmitting
two
>>independent signals??
>
>I forget what is the formal definition of 
>orthogonality.  I think it has to do with 
>the integral of the product of two signals 
>being equal to zero.  Something like that.
>
>>The reason I'm asking is that I'm trying to follow quadrature modulation
in
>>frequency domain, and I can see how in-phase or quadrature parts cancel
>>each other out and it's all fine, but shouldn't I be able to see
>>orthogonality if I just look at one side (positive or negative) of the
>>frequency domain? Is the negative frequency content just there to make
the
>>signal real or it's what actually makes quadrature modulation possible?
>
>I'm not exactly sure what you're asking here.
>Can you ask your questions by relating them 
>to specific figures in my book or specific 
>figures in my online qudrature tutorial article?
>
>[-Rick-]
>

Hi Rick, 

Ok, let's say we're in Matlab world and I have two independent real-value
baseband signals. If I multiply one by e^(j*w_c*t) and the other one by
e^(j*w_c*t + pi/2) and add the results, can I still retrieve the two
original messages from the this result?

As Tim said, I'm trying to figure out if I can do all my quadrature
modulation math without paying attention to the negative frequency part or
not.

I'll relate them to figures in your book once I get home. 	 

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> Hi Rick, 
> 
> Ok, let's say we're in Matlab world and I have two independent real-value
> 
> baseband signals. If I multiply one by e^(j*w_c*t) and the other one by
> 
> e^(j*w_c*t + pi/2) and add the results, can I still retrieve the two
> 
> original messages from the this result?
> 
> As Tim said, I'm trying to figure out if I can do all my quadrature
> 
> modulation math without paying attention to the negative frequency part or
> 
> not.
> 
> I'll relate them to figures in your book once I get home. 	 
> 
Maybe this will help you:
You have to real signals (with equal bandwidth, BW), x1(t) and x2(t). Combine them to a complex signal, x12(t) = x1(t) + j*x2(t)
Translate this signal, using a mixer: x12t(t) = x12(t) * exp(j*2*pi*f*t)
This signal has no negative frequencies if f > BW, and you can take the real part of this signal like:
real(x12t(t)) = x1(t) * cos(2*pi*f*t) - x2(t) * sin(2*pi*f*t)

To avoid aliasing the sampling rate, Fs, must be: Fs > 2 * (BW+f)
---
ww