On 25.11.2015 15:25, Steve Pope wrote:
> kaz <37480@DSPRelated> wrote:
>
>> [attribution lost] wrote,
>
>>> 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.
>
>> Does this apply to say sine/cosine waveforms. I generated 2^20 samples
>> each. multiplied them and integrated but can't see the above definition
>> apply. What am I missing?
>
> Except for truncation errors you should get zero correlation
> between a sine and a cosine of the same frequency.

... and between any sine or cosine of different (positive)frequencies

>
> If you get a non-zero value, compare it to the correlation of
> just the sine signal with itself; the latter value should be
> much much larger.
>
> Steve
>

>Hello,
>
>I would like to know definition of orthogonal signals and why they are
>significant in communication?
>
>Thanks, 
>---------------------------------------
>Posted through http://www.DSPRelated.com

Orthogonal signals integrate to zero, interchangeably their dot product
are zero. We can obtain find them by solving Sturm–Liouville
differential equations.
They are important in detection. when we want to demodulate the signal to
detect the symbols, this orthogonality helps us to separate the I and Q.
If we multiply the received signal by one of the basis functions all other
terms will add up to zero.   


---------------------------------------
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On Sat, 28 Nov 2015 14:36:15 -0600, "kaz" <37480@DSPRelated> wrote:

>>>The context helps a lot, as there were otherwise multiple ways to
>>>interpret what you were asking, and therefore going off in a less
>>>relevant direction.
>>
>>Dear Eric,
>>
>>I understand. I will take care in future postings.
>>
>>>Remember that a subcarrier's modulation is constant for the duration
>>>of the "symbol", i.e., the entire FFT length, and as long as that is
>>>true the magnitude and phase of the subcarrier can be whatever you
>>>want it to be.
>>
>>While we are on the OFDM and FFT topic, I would like clarify something
>>about FFT used for OFDM. Is iFFT specifically designed to handle 15 KHz
>>subcarrier spacing and sub-carrier bandwidth? If not, how is this taken
>>care?
>>
>>---------------------------------------
>>Posted through http://www.DSPRelated.com
>
>In your other thread on ifft I posted:
>
>15KHz comes from 7.68MHz/512 (for lte 5MHz as example)
>
>so what determines 15KHz????
>
>Kaz

I answered previously with the technical implementation answer, but it
occurred to me that you might be asking why 15kHz was chosen for the
subcarriers.   The short answer is because the spec says so.   My
guess as to why the spec says so is that it provided a good solution
for the tradeoff space that they (i.e., the standard working group)
were managing given the channel models for the expected environments.

Too narrow and the system becomes susceptible to phase noise, too wide
and the subcarrier fading in the encountered channels may not be flat
(which defeats the purpose of OFDM).  


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

On Sat, 28 Nov 2015 14:36:15 -0600, "kaz" <37480@DSPRelated> wrote:

>>>The context helps a lot, as there were otherwise multiple ways to
>>>interpret what you were asking, and therefore going off in a less
>>>relevant direction.
>>
>>Dear Eric,
>>
>>I understand. I will take care in future postings.
>>
>>>Remember that a subcarrier's modulation is constant for the duration
>>>of the "symbol", i.e., the entire FFT length, and as long as that is
>>>true the magnitude and phase of the subcarrier can be whatever you
>>>want it to be.
>>
>>While we are on the OFDM and FFT topic, I would like clarify something
>>about FFT used for OFDM. Is iFFT specifically designed to handle 15 KHz
>>subcarrier spacing and sub-carrier bandwidth? If not, how is this taken
>>care?
>>
>>---------------------------------------
>>Posted through http://www.DSPRelated.com
>
>In your other thread on ifft I posted:
>
>15KHz comes from 7.68MHz/512 (for lte 5MHz as example)
>
>so what determines 15KHz????
>
>Kaz

In the modulator, the length of the FFT and the sample rate via the
usual relationship of df = fs/N, where df is the bin spacing, fs is
the sample rate and N is the FFT size.   It's no different than
sorting out the bin width for any other FFT application.

Since the spec dictates a 15kHz subcarrier spacing, for the N = 512
case the effective output sample rate (barring interpolation for
signal conditioning, etc.), is then fs = 15e3*512 = 7.68MHz.

There's a table of the rates here:

http://lteuniversity.com/ask_the_expert/f/59/t/2636.aspx


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

>>The context helps a lot, as there were otherwise multiple ways to
>>interpret what you were asking, and therefore going off in a less
>>relevant direction.
>
>Dear Eric,
>
>I understand. I will take care in future postings.
>
>>Remember that a subcarrier's modulation is constant for the duration
>>of the "symbol", i.e., the entire FFT length, and as long as that is
>>true the magnitude and phase of the subcarrier can be whatever you
>>want it to be.
>
>While we are on the OFDM and FFT topic, I would like clarify something
>about FFT used for OFDM. Is iFFT specifically designed to handle 15 KHz
>subcarrier spacing and sub-carrier bandwidth? If not, how is this taken
>care?
>
>---------------------------------------
>Posted through http://www.DSPRelated.com

In your other thread on ifft I posted:

15KHz comes from 7.68MHz/512 (for lte 5MHz as example)

so what determines 15KHz????

Kaz
---------------------------------------
Posted through http://www.DSPRelated.com

On Sat, 28 Nov 2015 12:11:46 -0600, "Sharan123" <99077@DSPRelated>
wrote:

>>The context helps a lot, as there were otherwise multiple ways to
>>interpret what you were asking, and therefore going off in a less
>>relevant direction.
>
>Dear Eric,
>
>I understand. I will take care in future postings.
>
>>Remember that a subcarrier's modulation is constant for the duration
>>of the "symbol", i.e., the entire FFT length, and as long as that is
>>true the magnitude and phase of the subcarrier can be whatever you
>>want it to be.
>
>While we are on the OFDM and FFT topic, I would like clarify something
>about FFT used for OFDM. Is iFFT specifically designed to handle 15 KHz
>subcarrier spacing and sub-carrier bandwidth? If not, how is this taken
>care?

The size of the FFT and the output sample rate.


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

>The context helps a lot, as there were otherwise multiple ways to
>interpret what you were asking, and therefore going off in a less
>relevant direction.

Dear Eric,

I understand. I will take care in future postings.

>Remember that a subcarrier's modulation is constant for the duration
>of the "symbol", i.e., the entire FFT length, and as long as that is
>true the magnitude and phase of the subcarrier can be whatever you
>want it to be.

While we are on the OFDM and FFT topic, I would like clarify something
about FFT used for OFDM. Is iFFT specifically designed to handle 15 KHz
subcarrier spacing and sub-carrier bandwidth? If not, how is this taken
care?

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

On Fri, 27 Nov 2015 09:11:09 -0600, "Sharan123" <99077@DSPRelated>
wrote:

>>On Thu, 26 Nov 2015 07:05:41 -0600, Sharan123 wrote:
>>
>>> Thanks, everyone
>>> 
>>> I have a couple of follow-up questions based on responses above ...
>>> 
>>> 1) if we take 2 orthogonal signals and then multiply them individually
>>> with some other signal then I assume that the resulting signals
>maintain
>>> orthogonality. Is this correct?
>>
>>Ooh, good question.
>>
>>In general, no.  For a lot of practical problems, yes -- this is how 
>>modulation works.  But it has to be designed in (or inherited from 
>>something that's worked for years).
>
>Dear Tim & others,
>
>My question above comes from what I have been reading about OFDM.
>
>So, essentially, we have a bunch of inputs and these get modulated by
>sub-carriers inside OFDM modulator and what we get orthogonal signal for
>each sub-carrier. So, I assumed that multiplying two orthogonal signals
>using arbitrary signals will retain orthogonality of the signals. 
>
>I have seen conflicting responses above ...

The context helps a lot, as there were otherwise multiple ways to
interpret what you were asking, and therefore going off in a less
relevant direction.

Subcarriers in OFDM are orthogonal to each other because the basis
functions of the DFT are orthogonal to each other, so each bin output
is orthogonal to the other bins.   So if you're asking whether the
modulation of a particular subcarrier affects any of the others, it
does not because the orthogonality is assured by the FFT.

One could also spread the subcarriers far apart from each other, so
that they obtain frequency orthogonality just by having sufficient
spacing between them.   The advantage of using the FFT is that they
are packed in frequency essentially as tightly as possible so that
much less bandwidth is required, i.e., no guard bands between the
subcarriers.

Remember that a subcarrier's modulation is constant for the duration
of the "symbol", i.e., the entire FFT length, and as long as that is
true the magnitude and phase of the subcarrier can be whatever you
want it to be.


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

>On Thu, 26 Nov 2015 07:05:41 -0600, Sharan123 wrote:
>
>> Thanks, everyone
>> 
>> I have a couple of follow-up questions based on responses above ...
>> 
>> 1) if we take 2 orthogonal signals and then multiply them individually
>> with some other signal then I assume that the resulting signals
maintain
>> orthogonality. Is this correct?
>
>Ooh, good question.
>
>In general, no.  For a lot of practical problems, yes -- this is how 
>modulation works.  But it has to be designed in (or inherited from 
>something that's worked for years).

Dear Tim & others,

My question above comes from what I have been reading about OFDM.

So, essentially, we have a bunch of inputs and these get modulated by
sub-carriers inside OFDM modulator and what we get orthogonal signal for
each sub-carrier. So, I assumed that multiplying two orthogonal signals
using arbitrary signals will retain orthogonality of the signals. 

I have seen conflicting responses above ...
---------------------------------------
Posted through http://www.DSPRelated.com

On Thu, 26 Nov 2015 07:05:41 -0600, Sharan123 wrote:

> Thanks, everyone
> 
> I have a couple of follow-up questions based on responses above ...
> 
> 1) if we take 2 orthogonal signals and then multiply them individually
> with some other signal then I assume that the resulting signals maintain
> orthogonality. Is this correct?

Ooh, good question.

In general, no.  For a lot of practical problems, yes -- this is how 
modulation works.  But it has to be designed in (or inherited from 
something that's worked for years).

> 2) From the posts above, I understand that if a transmitted signal is
> composed of orthogonal signals then it is easier to recover individual
> signals. Is this correct?

Pretty much.  More importantly, you waste less transmitted power.

If you're serious about this stuff you may want to start studying 
communications theory.  It's not a trivial subject -- it's usually 
something you start studying in your 3rd year of electronics engineering, 
and it's built on a lot of the preceding stuff.  But if you take a formal 
course of study you'll get ALL of the relevant detail.

-- 
www.wescottdesign.com