Quadrature Signals: Complex, But Not Complicated by Richard Lyons -- j operator implementation

Dear All,
I have just read this excellent article "Quadrature Signals: Complex, But
Not Complicated by Richard Lyons", and feel enlightened by Dr. Lyons'
explanation of this quadrature concept.

One question arise regarding the implementation of j operator.
As shown in Figure 20 in this article, it is explained that the j operator
is implemented by treating in-phase signal and quadrature-phase signal to
be orthogonal to each other.

It is very clear in the case where we can use 2 cables to independently
convey i-phase and q-phase signal separately, and then the j operator can
be implemented by treating i-phase signal as horizontal input and q-phase
signal as vertical input to the oscilloscope.

However, in the case of wireless transmission, how can we implement this j
operator?
My guess is, by conveying i-phase in the horizontally polarized
electro-magnetic wave and conveying q-phase in the vertically polarized
electro-magnetic wave, then we can have a perpendicular i, q-phase
signal.

Is my guess correct? Are there any other ways to implement j operator in
wireless transmission.
Thank you for your expertise and time.

Best regards,
Ivan Setiawan

Hello,

real and imaginary part describe the amplitude of a sine and cosine wave
at radio frequency. 
An alternative way to put it is that we have two parameters for a
sinusoidal wave at a given frequency, the amplitude and the angle.

BTW, polarization isn't a bad bet either, but not in a DSP forum :)
It is correct, we can transmit two independent streams via polarization,
but that's not what's meant here, IMO.

check figure 14.

"mnentwig" <mnentwig@elisanet.fi> writes:

> BTW, polarization isn't a bad bet either, but not in a DSP forum :)
> It is correct, we can transmit two independent streams via
> polarization,

Yep, and analog satellites did (do?) just that to get more usage
out of a frequency band.

Ain't E&M cool?
-- 
%  Randy Yates                  % "She has an IQ of 1001, she has a jumpsuit
%% Fuquay-Varina, NC            %            on, and she's also a telephone."
%%% 919-577-9882                % 
%%%% <yates@ieee.org>           %        'Yours Truly, 2095', *Time*, ELO   
http://www.digitalsignallabs.com

Hello,
Thank you for your explanation.

>real and imaginary part describe the amplitude of a sine and cosine wave
>at radio frequency. 

From figure 14, as you mentioned, I think the in-phase and q-phase
components can be extracted by multiplying and integrating with cos and
sin, respectively.
Thus, a separate 'perpendicular' wireless carrier is not needed.

Thanks,
ivan

On Mon, 07 Jan 2008 05:42:25 -0600, "setiawan" <ivans@yahoo.co.jp>
wrote:

>Dear All,

Hi Ivan,

>I have just read this excellent article "Quadrature Signals: Complex, But
>Not Complicated by Richard Lyons", and feel enlightened by Dr. Lyons'
>explanation of this quadrature concept.

I don't have a Ph.D.  (But I did formally graduate 
from high school.  Whew.  The twelfth grade was the 
longest three years of my life!)  So please 
call me "Rick".  My friends do.

>One question arise regarding the implementation of j operator.
>As shown in Figure 20 in this article, it is explained that the j operator
>is implemented by treating in-phase signal and quadrature-phase signal to
>be orthogonal to each other.
>
>It is very clear in the case where we can use 2 cables to independently
>convey i-phase and q-phase signal separately, and then the j operator can
>be implemented by treating i-phase signal as horizontal input and q-phase
>signal as vertical input to the oscilloscope.
>
>However, in the case of wireless transmission, how can we implement this j
>operator?
>My guess is, by conveying i-phase in the horizontally polarized
>electro-magnetic wave and conveying q-phase in the vertically polarized
>electro-magnetic wave, then we can have a perpendicular i, q-phase
>signal.
>
>Is my guess correct? Are there any other ways to implement j operator in
>wireless transmission.
>Thank you for your expertise and time.

Oh shoot.  My experience in communications is 
shamefully limited, but your notion of the two different 
polarizations conveying the I and Q signals separately 
seems reasonable to me.

In that little "Complex, But Not Complicated" paper 
I stressed the idea that we needed two cables to transmit 
an analog quadrature signal, or two (multi-conductor) 
ribbon cables to transmit a discrete (sampled) 
quadrature signal. However, our DSP pal Clay Turner 
reminded me that "in the general case" we need 
two "channels" to transmit a quadrature signal.

So Clay's point (I think) is: if you can create any 
signal (analog or digital) that contains two 
separate (independent) parts, two parameters, 
two "channels", then you should be able to treat 
that signal as a quadrature signal.   

Of course, the two "parts" of the signal must be 
orthogonal, meaning that changing the value of one 
part has no effect on the value of the other part.
(Sorry for using the vague term "part".  I can't think 
of a better word right now.)

Good Luck,
[-Rick-]

Rick Lyons wrote:
> Oh shoot.  My experience in communications is 
> shamefully limited, but your notion of the two different 
> polarizations conveying the I and Q signals separately 
> seems reasonable to me.

A writer with limited experience in communications? Weird. :-)

Steve

>I don't have a Ph.D.  (But I did formally graduate 
>from high school.  Whew.  The twelfth grade was the 
>longest three years of my life!)  So please 
>call me "Rick".  My friends do.

Dear Rick :)
Sorry for my misunderstanding, but I am sure that you are a 'Sensei' in
this field.

>In that little "Complex, But Not Complicated" paper 
>I stressed the idea that we needed two cables to transmit 
>an analog quadrature signal, or two (multi-conductor) 
>ribbon cables to transmit a discrete (sampled) 
>quadrature signal. However, our DSP pal Clay Turner 
>reminded me that "in the general case" we need 
>two "channels" to transmit a quadrature signal.
>
>So Clay's point (I think) is: if you can create any 
>signal (analog or digital) that contains two 
>separate (independent) parts, two parameters, 
>two "channels", then you should be able to treat 
>that signal as a quadrature signal.   

This confirms again my understanding. Thank you very much.
A perpendicular polarization is A way to create quadrature signal,
regardless it is usable/feasible or not.

Best regards,
Ivan

>Yep, and analog satellites did (do?) just that to get more usage
>out of a frequency band.
>
>Ain't E&M cool?

Oh yes it is. Few other disciplines can match EM in terms of integral
signs per page :)
But I still believe that 99% of the cases found in and around this forum
(and in a typical communications course) will relate to sine / cosine
waves on a carrier frequency.

Totally OT, but my radio-controlled helicopter uses polarization diversity
with two antennas at 90 deg angle...

On Wed, 09 Jan 2008 01:59:18 -0600, "mnentwig" <mnentwig@elisanet.fi>
wrote:

>>Yep, and analog satellites did (do?) just that to get more usage
>>out of a frequency band.
>>
>>Ain't E&M cool?
>
>Oh yes it is. Few other disciplines can match EM in terms of integral
>signs per page :)
>But I still believe that 99% of the cases found in and around this forum
>(and in a typical communications course) will relate to sine / cosine
>waves on a carrier frequency.
>
>Totally OT, but my radio-controlled helicopter uses polarization diversity
>with two antennas at 90 deg angle...

Diversity combining with polarized antennas makes some sense for
increasing range in a multipath environment.  That's sort of the idea
behind rabbit ear antennas for VHF TV.

Eric Jacobsen
Minister of Algorithms
Abineau Communications
http://www.ericjacobsen.org