Orthogonol signals

Hello,

I would like to know definition of orthogonal signals and why they are
significant in communication?

Thanks, 
---------------------------------------
Posted through http://www.DSPRelated.com

Sharan123 <99077@dsprelated> wrote:
 
> I would like to know definition of orthogonal signals and why they are
> significant in communication?

Orthogonal means that if you multiply them, multiply by a weight
function (which might be one) and integrate over the appropriate
interval, the result is zero.

In the case of signals, it makes them easy to separate.

-- glen

On Tue, 24 Nov 2015 07:50:30 -0600, Sharan123 wrote:

> Hello,
> 
> I would like to know definition of orthogonal signals and why they are
> significant in communication?
> 

Two signals are orthogonal if you can multiply them together, average the 
result, and get exactly zero.  (This is what Glen said, but I like my 
wording better).

In radio you can use this by generating a bunch of orthogonal signals at 
the transmitter, then have a bunch of different receivers that each 
multiply the signal at their antenna by their one desired signal -- the 
result is that all the other signals are rejected, but the one desired 
signal is received.  The superheterodyne receiver (like a broadcast-band 
AM or FM receiver) is just one way of achieving this -- digital cell 
phones have another way that's far more complicated (and uses different 
signals) but has significant advantages for cell phones.

-- 

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

On Tue, 24 Nov 2015 07:50:30 -0600, "Sharan123" <99077@DSPRelated>
wrote:

>Hello,
>
>I would like to know definition of orthogonal signals and why they are
>significant in communication?
>
>Thanks, 

The upshot of orthogonality is that if you do something (filter,
multiply, amplify, attenuate, equalize, rhinoplasty, whatever), a
signal that is orthogonal to another signal, only the signal being
operated on is affected.   Orthogonality makes things functionally
independent, and in communications this means that information put in
one signal is not disturbed or affected by the other signals, and vice
versa.

There are many, many types of orthogonality.    A simple one is
orthogonality in time, where one signal is transmitted during a
particular time slot, and  a different signal in a different time
slot.   Frequency orthogonality is also pretty simple, where (usually)
one TV station on a particular channel isn't interfered with by
signals on other channels.

In a much more detailed sense, the I and Q channels of a single signal
are orthogonal, and carry independent information.   Likewise the
subcarriers of an OFDM signal, or CDMA signals spread with codes that
are all mutually orthogonal to each other.


Eric Jacobsen
Anchor Hill Communications
http://www.anchorhill.com

On Tuesday, November 24, 2015 at 8:50:34 AM UTC-5, Sharan123 wrote:
> Hello,
> 
> I would like to know definition of orthogonal signals and why they are
> significant in communication?
> 
> Thanks, 
> ---------------------------------------
> Posted through http://www.DSPRelated.com

The definition involves a stupid integral, but you can look that up.  The relevance is independence, but you will need to spend a lot of time thinking about that

On Tuesday, November 24, 2015 at 8:50:34 AM UTC-5, Sharan123 wrote:
> Hello,
> 
> I would like to know definition of orthogonal signals and why they are
> significant in communication?
> 
> Thanks, 
> ---------------------------------------
> Posted through http://www.DSPRelated.com


well, here's my spin:

first consider a "signal" as an element of a set of signals we call a "metric space", more specifically a "Hilbert space".

a metric space is a mathematical construct where an individual "signal" (in our case a discrete-time or continuous-time function) is like a single "point" in the space and there is a means of measuring the distance between points such that if the two signals are identical, the distance is zero.

a "Hilbert space" is a metric space that has this thing called an "inner product" which is very similar to the "dot product" we see in cartesian space.

two signals are "orthogonal" if their inner product is zero.  just like in cartesian space, two vectors are orthogonal if their dot product is zero.

that's my spin.

[sorry i have to use Google Groups for a while.  it's what happens when i change computers.  i also have to use my webmail for email.  no mail client.  i **hate** "progress".]

r b-j

On Tuesday, November 24, 2015 at 5:00:36 PM UTC-5, robert bristow-johnson wrote:
> On Tuesday, November 24, 2015 at 8:50:34 AM UTC-5, Sharan123 wrote:
> > Hello,
> > 
> > I would like to know definition of orthogonal signals and why they are
> > significant in communication?
> > 
> > Thanks, 
> > ---------------------------------------
> > Posted through http://www.DSPRelated.com
> 
> 
> well, here's my spin:
> 
> first consider a "signal" as an element of a set of signals we call a "metric space", more specifically a "Hilbert space".
> 
> a metric space is a mathematical construct where an individual "signal" (in our case a discrete-time or continuous-time function) is like a single "point" in the space and there is a means of measuring the distance between points such that if the two signals are identical, the distance is zero.
> 
> a "Hilbert space" is a metric space that has this thing called an "inner product" which is very similar to the "dot product" we see in cartesian space.
> 
> two signals are "orthogonal" if their inner product is zero.  just like in cartesian space, two vectors are orthogonal if their dot product is zero.
> 
> that's my spin.
> 
> [sorry i have to use Google Groups for a while.  it's what happens when i change computers.  i also have to use my webmail for email.  no mail client.  i **hate** "progress".]
> 
> r b-j

OK I modify my advice.... you need to think about this stuff while on drugs

Tim Wescott <seemywebsite@myfooter.really> wrote:
> On Tue, 24 Nov 2015 07:50:30 -0600, Sharan123 wrote:
 
>> I would like to know definition of orthogonal signals and why they are
>> significant in communication?
 
> Two signals are orthogonal if you can multiply them together, average the 
> result, and get exactly zero.  (This is what Glen said, but I like my 
> wording better).

In the more general case, you have to allow for a weight function.
For signals on wires, that will normally be one.

In cylindrical coordinates, Bessel functions are often needed for
the radial term, and the weight function is usually r. (That is,
the radial coordinate.) There are also functions that are orthogonal
in spherical coordinates, such as those used to describe bonding
electrons in chemistry.

I suspect that spherical and cylindrical coordinates come up
in radio transmission, but for signal on wires they shouldn't
be needed.
 
> In radio you can use this by generating a bunch of orthogonal signals at 
> the transmitter, then have a bunch of different receivers that each 
> multiply the signal at their antenna by their one desired signal -- the 
> result is that all the other signals are rejected, but the one desired 
> signal is received.  The superheterodyne receiver (like a broadcast-band 
> AM or FM receiver) is just one way of achieving this -- digital cell 
> phones have another way that's far more complicated (and uses different 
> signals) but has significant advantages for cell phones.

Also for the FM stereo subcarrier and NTSC color subcarriers.

-- glen

On Wed, 25 Nov 2015 01:52:53 +0000, glen herrmannsfeldt wrote:

> Tim Wescott <seemywebsite@myfooter.really> wrote:
>> On Tue, 24 Nov 2015 07:50:30 -0600, Sharan123 wrote:
>  
>>> I would like to know definition of orthogonal signals and why they are
>>> significant in communication?
>  
>> Two signals are orthogonal if you can multiply them together, average
>> the result, and get exactly zero.  (This is what Glen said, but I like
>> my wording better).
> 
> In the more general case, you have to allow for a weight function. For
> signals on wires, that will normally be one.

You're thinking orthonormal.  Orthogonality just demands zero between 
signals.  Orthonormal demands zero between signals, and a unity result 
from multiplying a signal by itself.

-- 

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

Tim Wescott <seemywebsite@myfooter.really> wrote:

(Tim wrote)
>>> Two signals are orthogonal if you can multiply them together, average
>>> the result, and get exactly zero.  (This is what Glen said, but I like
>>> my wording better).
 
>> In the more general case, you have to allow for a weight function. For
>> signals on wires, that will normally be one.
 
> You're thinking orthonormal.  Orthogonality just demands zero between 
> signals.  Orthonormal demands zero between signals, and a unity result 
> from multiplying a signal by itself.

Well, that, too.

But for example, finding the vibrational modes of a circular drum,
you need a Bessel function expansion, with orthogonality

\integral_0^1 J_m(ar) J_m(br) r dr = 0    a not equal to b.

With J_m(a) = J_m(b) = 0.

The extra r comes from doing the integral in cylindrical
coordinates. (Or radial coordinates, same r.)

http://www.hit.ac.il/staff/benzionS/Differential.Equations/Orthogonality_of_Bessel_functions.htm

-- glen