What makes quadrature mixing possible?

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? 
How did we implement the j-operator? Are we exploiting the fact that sin
and cos carriers are orthogonal? If we had another pair of orthogonal
signals that didn't look like sin or cos at all, could we use them to do
the same thing and modulate two independent I and Q signals on one physical
channel? Do sin and cos have any significance?

	 

_____________________________		
Posted through www.DSPRelated.com

miladsp 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?
> How did we implement the j-operator? Are we exploiting the fact that sin
> and cos carriers are orthogonal? If we had another pair of orthogonal
> signals that didn't look like sin or cos at all, could we use them to do
> the same thing and modulate two independent I and Q signals on one physical
> channel? Do sin and cos have any significance?
>
> 	
>
> _____________________________		
> Posted through www.DSPRelated.com
>

Sin and cos have the property that the Hilbert transform operator and 
its inverse map them  onto each other, give or take.

Have you found this yet? It's from Rick Lyons, a poobah on this froup.

http://www.dspguru.com/sites/dspguru/files/QuadSignals.pdf

-- 
Les Cargill

On Sun, 31 Aug 2014 12:17:17 -0500, miladsp 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?

Mostly we're exploiting some mathematical tricks, but the underlying 
physical reality is that sine and cosine are orthogonal.

> Am I right in thinking that
> we're essentially transmitting a complex signal using a real signal?

Arguably yes.  Or no.  How ornery are you feeling?

You can choose to view quadrature mixing as a process that turns a complex 
baseband signal into a real signal around some non-zero frequency, or visa-
versa.

Or you can choose to to view quadrature mixing in the sense that all the 
signals are always real, and they're just being modeled by complex numbers 
(this is my preferred view).

Or you can choose a view that you have an inphase signal and a quadrature 
signal, that they are both always real, and that complex numbers are 
complete bulls**t dreamed up by mathematicians in a lame attempt to make 
themselves look smart, but it's all unnecessary because you can make the 
math work using trig identities.

Pick your poison.

> How did we implement the j-operator?

We don't, really.  See my response to your last question.

> Are we exploiting the fact that sin
> and cos carriers are orthogonal? 

Yes, but do keep in mind that unless you have a way to phase-align your 
local carrier with the transmitter, it's probably more proper to say that 
we're exploiting the fact that a sine wave and a cosine wave are 
orthogonal to each other.

> If we had another pair of orthogonal
> signals that didn't look like sin or cos at all, could we use them to do
> the same thing and modulate two independent I and Q signals on one
> physical channel?

Yes.  This is basically what spread-spectrum does.  Direct-sequence spread 
spectrum is the closest to your statement, in that it uses a sequence 
that's orthogonal to everything else, but isn't orthogonal to itself.

> Do sin and cos have any significance?

Yes.  Many useful structures in the physical world tend to act reasonably 
simply in the frequency domain -- antennas act like bandpass filters, 
circuits designed for baseband tend to act like fairly simple lowpass 
filters, it is easy to design circuits to act like a particular sort of 
circuit, etc.

This is not true of domains based on other basis functions (such as spread-
spectrum, or domains based on Walsh functions, etc.).  So when you're 
working with a signal that needs to be impressed on a voltage, then 
transmitted through the vacuum as electromagnetic waves (or through some 
physical medium as sound waves or other physical phenomenon), doing your 
analysis in terms of the frequency domain -- which, in turn, means you're 
doing your analysis in terms of sines and cosines -- makes the math far 
easier.

-- 

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

>miladsp 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?
>> How did we implement the j-operator? Are we exploiting the fact that
sin
>> and cos carriers are orthogonal? If we had another pair of orthogonal
>> signals that didn't look like sin or cos at all, could we use them to
do
>> the same thing and modulate two independent I and Q signals on one
physical
>> channel? Do sin and cos have any significance?
>>
>> 	
>>
>> _____________________________		
>> Posted through www.DSPRelated.com
>>
>
>Sin and cos have the property that the Hilbert transform operator and 
>its inverse map them  onto each other, give or take.
>
>Have you found this yet? It's from Rick Lyons, a poobah on this froup.
>
>http://www.dspguru.com/sites/dspguru/files/QuadSignals.pdf
>
>-- 
>Les Cargill
>

Thanks Les, yes, it's the best thing I've found on the topic.
	 

_____________________________		
Posted through www.DSPRelated.com

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.

First they start with an RGB signal, gamma correct them, and generate
the luminance signal, Y, (an appropriate linear combination).
(The values are set such that blue and red look appropriatly dark,
on a black and white TV set.)

The generate (R-Y) and (B-Y). You can see how to regenerate R, G, 
and B from Y, (R-Y), and (B-Y). If you modulate quadrature signals
with an AM supressed carrier modulator, you end up with a signal
where the phase indicates color (hue) and amplitude saturation.

But that isn't how NTSC does it. NTSC determined that the human
visual system has different resolution for different color, and,
if you graph it on a color wheel, not parallel to the R, G, or B
axis.  So, (R-Y) and (B-Y) are appropriatly matrixed to generate
the I and Q signals, where I is the orange-blue axis and Q is
along the purple-green axis. Then I and Q are filtered to reduce
the bandwidth, 1.3MHz for I, 0.4MHz for Q. 

The result of the (R-Y) and (B-Y) to I and Q matrix is a rotation
in color space. To get full color resolution, one should decode
the I and Q signal, filter them appropriately, then dematrix
to get (R-Y) and (B-Y). 

Turns out, though, that you can cheat if you don't need the full
resolution. You can decode on the (R-Y) and (B-Y) axes instead
of the I and Q axes, filter both down to 0.4MHz. You don't get 
the full resolution, but close enough.

Now, to answer your question, there is one more requirement:
you need a phase reference. Maybe this is the answer you were
looking for. Just given the signal, you can't separate the I
and Q (or (R-Y) and (B-Y)) components. For NTSC, just before
each scan line a few cycles of the reference carrier with the
phase appropriate for green are supplied. A high-Q filter
(or oscillator, same thing) then generates a phase reference
for the whole scan line. One result is that 3.579545MHz is
the most common frequency for quart crystals. 

The FM stereo subcarrier is another exmaple, and interesting
in different ways.

-- glen

(snip, I wrote)
> The chrominance subcarrier in an NTSC video signal is an interesting
> example.

Oh, I forgot:  https://en.wikipedia.org/wiki/YIQ

That includes the matrix coefficients and descriptions
of color space. It doesn't seem to include the (R-Y) (B-Y)
decoding, on pretty much every color TV set until just before
digital took over.  Ones doing IQ decoding were advertized as EDTV,
enhanced definition. 

But for people who watch on VHS tapes recorded at the slowest
tape speed, 0.4MHz is way more color resolution then they need.

-- glen

>On Sun, 31 Aug 2014 12:17:17 -0500, miladsp 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?
>
>Mostly we're exploiting some mathematical tricks, but the underlying 
>physical reality is that sine and cosine are orthogonal.
>
>> Am I right in thinking that
>> we're essentially transmitting a complex signal using a real signal?
>
>Arguably yes.  Or no.  How ornery are you feeling?
>
>You can choose to view quadrature mixing as a process that turns a complex

>baseband signal into a real signal around some non-zero frequency, or
visa-
>versa.
>
>Or you can choose to to view quadrature mixing in the sense that all the 
>signals are always real, and they're just being modeled by complex numbers

>(this is my preferred view).
>
>Or you can choose a view that you have an inphase signal and a quadrature

>signal, that they are both always real, and that complex numbers are 
>complete bulls**t dreamed up by mathematicians in a lame attempt to make 
>themselves look smart, but it's all unnecessary because you can make the 
>math work using trig identities.
>
>Pick your poison.
>
>> How did we implement the j-operator?
>
>We don't, really.  See my response to your last question.
>
>> Are we exploiting the fact that sin
>> and cos carriers are orthogonal? 
>
>Yes, but do keep in mind that unless you have a way to phase-align your 
>local carrier with the transmitter, it's probably more proper to say that

>we're exploiting the fact that a sine wave and a cosine wave are 
>orthogonal to each other.
>
>> If we had another pair of orthogonal
>> signals that didn't look like sin or cos at all, could we use them to
do
>> the same thing and modulate two independent I and Q signals on one
>> physical channel?
>
>Yes.  This is basically what spread-spectrum does.  Direct-sequence spread

>spectrum is the closest to your statement, in that it uses a sequence 
>that's orthogonal to everything else, but isn't orthogonal to itself.
>
>> Do sin and cos have any significance?
>
>Yes.  Many useful structures in the physical world tend to act reasonably

>simply in the frequency domain -- antennas act like bandpass filters, 
>circuits designed for baseband tend to act like fairly simple lowpass 
>filters, it is easy to design circuits to act like a particular sort of 
>circuit, etc.
>
>This is not true of domains based on other basis functions (such as
spread-
>spectrum, or domains based on Walsh functions, etc.).  So when you're 
>working with a signal that needs to be impressed on a voltage, then 
>transmitted through the vacuum as electromagnetic waves (or through some 
>physical medium as sound waves or other physical phenomenon), doing your 
>analysis in terms of the frequency domain -- which, in turn, means you're

>doing your analysis in terms of sines and cosines -- makes the math far 
>easier.
>
>-- 
>
>Tim Wescott
>Wescott Design Services
>http://www.wescottdesign.com
>

Thanks Tim. Very useful response. 

Does it make sense to say that Sin and Cos are special orthogonal signals
in the sense that they don't change the bandwidth of the baseband signal,
ttherefore you can think that the baseband signal was 2 dimensional (i.e.
complex) in the first place?

	 

_____________________________		
Posted through www.DSPRelated.com

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?	 

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Posted through www.DSPRelated.com

On Sun, 31 Aug 2014 17:21:53 -0500, miladsp wrote:

>>On Sun, 31 Aug 2014 12:17:17 -0500, miladsp 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?
>>
>>Mostly we're exploiting some mathematical tricks, but the underlying
>>physical reality is that sine and cosine are orthogonal.
>>
>>> Am I right in thinking that we're essentially transmitting a complex
>>> signal using a real signal?
>>
>>Arguably yes.  Or no.  How ornery are you feeling?
>>
>>You can choose to view quadrature mixing as a process that turns a
>>complex
> 
>>baseband signal into a real signal around some non-zero frequency, or
> visa-
>>versa.
>>
>>Or you can choose to to view quadrature mixing in the sense that all the
>>signals are always real, and they're just being modeled by complex
>>numbers
> 
>>(this is my preferred view).
>>
>>Or you can choose a view that you have an inphase signal and a
>>quadrature
> 
>>signal, that they are both always real, and that complex numbers are
>>complete bulls**t dreamed up by mathematicians in a lame attempt to make
>>themselves look smart, but it's all unnecessary because you can make the
>>math work using trig identities.
>>
>>Pick your poison.
>>
>>> How did we implement the j-operator?
>>
>>We don't, really.  See my response to your last question.
>>
>>> Are we exploiting the fact that sin and cos carriers are orthogonal?
>>
>>Yes, but do keep in mind that unless you have a way to phase-align your
>>local carrier with the transmitter, it's probably more proper to say
>>that
> 
>>we're exploiting the fact that a sine wave and a cosine wave are
>>orthogonal to each other.
>>
>>> If we had another pair of orthogonal signals that didn't look like sin
>>> or cos at all, could we use them to
> do
>>> the same thing and modulate two independent I and Q signals on one
>>> physical channel?
>>
>>Yes.  This is basically what spread-spectrum does.  Direct-sequence
>>spread
> 
>>spectrum is the closest to your statement, in that it uses a sequence
>>that's orthogonal to everything else, but isn't orthogonal to itself.
>>
>>> Do sin and cos have any significance?
>>
>>Yes.  Many useful structures in the physical world tend to act
>>reasonably
> 
>>simply in the frequency domain -- antennas act like bandpass filters,
>>circuits designed for baseband tend to act like fairly simple lowpass
>>filters, it is easy to design circuits to act like a particular sort of
>>circuit, etc.
>>
>>This is not true of domains based on other basis functions (such as
> spread-
>>spectrum, or domains based on Walsh functions, etc.).  So when you're
>>working with a signal that needs to be impressed on a voltage, then
>>transmitted through the vacuum as electromagnetic waves (or through some
>>physical medium as sound waves or other physical phenomenon), doing your
>>analysis in terms of the frequency domain -- which, in turn, means
>>you're
> 
>>doing your analysis in terms of sines and cosines -- makes the math far
>>easier.
>>
>>--
>>
>>Tim Wescott Wescott Design Services http://www.wescottdesign.com
>>
>>
> Thanks Tim. Very useful response.
> 
> Does it make sense to say that Sin and Cos are special orthogonal
> signals in the sense that they don't change the bandwidth of the
> baseband signal,
> ttherefore you can think that the baseband signal was 2 dimensional
> (i.e.
> complex) in the first place?

It makes sense in the same way as saying that a penny is worth a cent 
because it's 1/100 of a dollar, and the circularity of the definition is 
just as shallow.

Bandwidth is a concept from Fourier analysis.  Fourier analysis uses sine 
waves as the basis function.  Using quadrature modulation via sine and 
cosine waves doesn't change the bandwidth, but more than anything else 
that's an artifact of the fact that sines and cosines are the basis 
functions of Fourier analysis.

-- 

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

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.

-- 

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