data storage/transfer through frequency transform

Hello,

I have a very basic question regarding transforming digital data into
frequency domain, transmitting and then recovering the data back.

1) Assume I have N data sources
2) Assume for the first data source, data geeration frequency is f
Similarly, f/2 for next data source, f/4 for next and so on
3) Now, I convert each of these data sources into individually into
frequency domain through frequency domain transform
4) This is done for all data sources resulting in frequency domain values
for all each data sources
5) I combine (this is the main part - is this possible?) frequency domain
result from individual frequency transform
6) I now transmit/store etc. this data
7) Later, since each of the data sources are limited to a specific
frequency range, I can apply filter and separate out individual data
sources
8) Recover the original data through frequency domain to time domain

Is this achievable/possible?

manishp <58525@dsprelated> wrote:
> Hello,

> I have a very basic question regarding transforming digital data into
> frequency domain, transmitting and then recovering the data back.

> 1) Assume I have N data sources
> 2) Assume for the first data source, data geeration frequency is f
> Similarly, f/2 for next data source, f/4 for next and so on
> 3) Now, I convert each of these data sources into individually into
> frequency domain through frequency domain transform
> 4) This is done for all data sources resulting in frequency domain values
> for all each data sources
> 5) I combine (this is the main part - is this possible?) frequency domain
> result from individual frequency transform

This is possible, but it usually requires a little space 
(unused frequency band) in between. That is, there is a little
waste in frequency space that you need to account for.

In the more usual case, the bandwidth of each channel is about
constant, and the guard band is about the same.

In your case, the bandwidth of the channels is decreasing
exponentially, but, usually, the guard band does not decrease
in the same way. 

Television channels are 6MHz wide. That was about right for an
analog TV signal, and is now used for digital TV. 

> 6) I now transmit/store etc. this data
> 7) Later, since each of the data sources are limited to a specific
> frequency range, I can apply filter and separate out individual data
> sources
> 8) Recover the original data through frequency domain to time domain

> Is this achievable/possible?

In the beginning of radio, there were no frequency domain circuits.
That was true, at least, in April 1912. 

But not so much later, AM broadcasting began with assigned
frequency bands for different stations. LC filters allowed one
to tune in a specific station.

It is still the usual way for wide band signals, but other
systems are often used for narrow band signals, such as cellular
telephones.

-- glen

On Mon, 01 Oct 2012 03:23:00 -0500, manishp wrote:

> Hello,
> 
> I have a very basic question regarding transforming digital data into
> frequency domain, transmitting and then recovering the data back.
> 
> 1) Assume I have N data sources
> 2) Assume for the first data source, data geeration frequency is f
> Similarly, f/2 for next data source, f/4 for next and so on 
> 3) Now, I
> convert each of these data sources into individually into frequency
> domain through frequency domain transform 
> 4) This is done for all data
> sources resulting in frequency domain values for all each data sources
> 5) I combine (this is the main part - is this possible?) frequency
> domain result from individual frequency transform 
> 6) I now
> transmit/store etc. this data 
> 7) Later, since each of the data sources
> are limited to a specific frequency range, I can apply filter and
> separate out individual data sources
> 8) Recover the original data through frequency domain to time domain
> 
> Is this achievable/possible?

Well, I'm going to disagree with Glen on this is a fundamental way:

You can't transmit data "in the frequency domain", or at least not 
without doing so in the time domain -- we live in the time domain, that's 
how we would transmit things.  The various frequency domains are 
mathematical concepts, designed to make some computations easier, but 
each one is a dual of a particular time domain: once something is 
determined in a frequency domain it is determined in a time domain, and 
visa versa.  You could do something like taking a chunk of signal's 
discrete Fourier transform, and transmit that -- but you'd be 
transmitting that DFT in the time domain, and reassembling it later.

So, I'm not sure if you're confusing heterodyning (which shifts a signal 
in frequency, but keeps it in the time domain), or actually transmitting 
a signal "in the frequency domain" which is impossible to do separately 
from this real time-domain world we live in, or what.

Perhaps give a top-level synopsis?  "I want to send data X to point B"?

-- 
My liberal friends think I'm a conservative kook.
My conservative friends think I'm a liberal kook.
Why am I not happy that they have found common ground?

Tim Wescott, Communications, Control, Circuits & Software
http://www.wescottdesign.com

The way I would look at your question / proposal would be like this:

First, moving things into the frequency domain, if done in some proper 
fashion so that neglibible "information" is lost, is simply a "mapping". 
  You are changing a set of numbers from one context into another.  And, 
you expect to be able to reverse the mapping to get everything back I 
should certainly think, eh?

The real question is, why would one want to do this?  The amount of 
information remaining the same means that the number of sampled per 
second has to stay the same.  So, there would appear to be little 
benefit in the adventure.

Perhaps changing the question a bit would be useful:
"How can I map data such that I gain some benefit in terms of signal to 
noise ratio, error rate, etc. given some communication channel?"

The answer to this type of question gets into what's called "coding" 
where the mapping being used (rather than a DFT for example) is somehow 
suited to the task at hand.  In general, one uses more bandwidth in a 
coding scheme.  That's what Shannon's "A Mathematical Theory of 
Communication" was about.

Fred

On 10/1/12 2:55 PM, Fred Marshall wrote:
>
> First, moving things into the frequency domain, if done in some proper
> fashion so that negligible "information" is lost, is simply a "mapping".

we can map to and from the frequency domain without losing information 
(except due to quantization) if we want to.

> You are changing a set of numbers from one context into another. And,
> you expect to be able to reverse the mapping to get everything back I
> should certainly think, eh?
>
> The real question is, why would one want to do this? The amount of
> information remaining the same means that the number of sampled per
> second has to stay the same. So, there would appear to be little benefit
> in the adventure.
>
> Perhaps changing the question a bit would be useful:
> "How can I map data such that I gain some benefit in terms of signal to
> noise ratio, error rate, etc. given some communication channel?"
>
> The answer to this type of question gets into what's called "coding"
> where the mapping being used (rather than a DFT for example) is somehow
> suited to the task at hand. In general, one uses more bandwidth in a
> coding scheme. That's what Shannon's "A Mathematical Theory of
> Communication" was about.

i do not believe that generally coding uses up more bandwidth.  unless i 
misunderstand what you're saying here, Fred.

one of the purposes of coding is to minimize the transmission bandwidth 
of a signal.  another purpose of coding is to put in enough redundancy 
that the receiver can detect and correct some data errors.  that, of 
course increases bandwidth, but when combined with the coding that 
decreases bandwidth, most of the time we get *both* error correction 
*and* decreased transmission bandwidth.

perhaps i just dunno what you intended to say.


-- 

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

On Mon, 01 Oct 2012 03:23:00 -0500, "manishp" <58525@dsprelated>
wrote:

>Hello,
>
>I have a very basic question regarding transforming digital data into
>frequency domain, transmitting and then recovering the data back.
>
>1) Assume I have N data sources
>2) Assume for the first data source, data geeration frequency is f
>Similarly, f/2 for next data source, f/4 for next and so on
>3) Now, I convert each of these data sources into individually into
>frequency domain through frequency domain transform
>4) This is done for all data sources resulting in frequency domain values
>for all each data sources
>5) I combine (this is the main part - is this possible?) frequency domain
>result from individual frequency transform
>6) I now transmit/store etc. this data
>7) Later, since each of the data sources are limited to a specific
>frequency range, I can apply filter and separate out individual data
>sources
>8) Recover the original data through frequency domain to time domain
>
>Is this achievable/possible?

What you're describing sounds a lot like OFDM as used in communication
systems (sometimes also called DMT).   You might look into that and
see how it applies to what you want to do.


Eric Jacobsen
Anchor Hill Communications
www.anchorhill.com

On Mon, 01 Oct 2012 18:00:53 -0400, robert bristow-johnson
<rbj@audioimagination.com> wrote:

>On 10/1/12 2:55 PM, Fred Marshall wrote:
>>
>> First, moving things into the frequency domain, if done in some proper
>> fashion so that negligible "information" is lost, is simply a "mapping".
>
>we can map to and from the frequency domain without losing information 
>(except due to quantization) if we want to.
>
>> You are changing a set of numbers from one context into another. And,
>> you expect to be able to reverse the mapping to get everything back I
>> should certainly think, eh?
>>
>> The real question is, why would one want to do this? The amount of
>> information remaining the same means that the number of sampled per
>> second has to stay the same. So, there would appear to be little benefit
>> in the adventure.
>>
>> Perhaps changing the question a bit would be useful:
>> "How can I map data such that I gain some benefit in terms of signal to
>> noise ratio, error rate, etc. given some communication channel?"
>>
>> The answer to this type of question gets into what's called "coding"
>> where the mapping being used (rather than a DFT for example) is somehow
>> suited to the task at hand. In general, one uses more bandwidth in a
>> coding scheme. That's what Shannon's "A Mathematical Theory of
>> Communication" was about.
>
>i do not believe that generally coding uses up more bandwidth.  unless i 
>misunderstand what you're saying here, Fred.
>
>one of the purposes of coding is to minimize the transmission bandwidth 
>of a signal.

That's "source coding", or compression.

>  another purpose of coding is to put in enough redundancy 
>that the receiver can detect and correct some data errors.

That's "channel coding", or error control coding or error correction
coding.


>  that, of 
>course increases bandwidth, but when combined with the coding that 
>decreases bandwidth, most of the time we get *both* error correction 
>*and* decreased transmission bandwidth.

That would be joint source-channel coding, which nobody has ever
really figured out how to do broadly or efficiently.   Nearly
universally the compression is done separately from the error
correction.

>
>perhaps i just dunno what you intended to say.

I think Fred was talking about channel coding.

>
>
>-- 
>
>r b-j                  rbj@audioimagination.com
>
>"Imagination is more important than knowledge."
>
>

Eric Jacobsen
Anchor Hill Communications
www.anchorhill.com

On Mon, 01 Oct 2012 18:00:53 -0400, robert bristow-johnson
<rbj@audioimagination.com> wrote:

>On 10/1/12 2:55 PM, Fred Marshall wrote:
>>
>> First, moving things into the frequency domain, if done in some proper
>> fashion so that negligible "information" is lost, is simply a "mapping".
>
>we can map to and from the frequency domain without losing information 
>(except due to quantization) if we want to.
>
>> You are changing a set of numbers from one context into another. And,
>> you expect to be able to reverse the mapping to get everything back I
>> should certainly think, eh?
>>
>> The real question is, why would one want to do this? The amount of
>> information remaining the same means that the number of sampled per
>> second has to stay the same. So, there would appear to be little benefit
>> in the adventure.
>>
>> Perhaps changing the question a bit would be useful:
>> "How can I map data such that I gain some benefit in terms of signal to
>> noise ratio, error rate, etc. given some communication channel?"
>>
>> The answer to this type of question gets into what's called "coding"
>> where the mapping being used (rather than a DFT for example) is somehow
>> suited to the task at hand. In general, one uses more bandwidth in a
>> coding scheme. That's what Shannon's "A Mathematical Theory of
>> Communication" was about.
>
>i do not believe that generally coding uses up more bandwidth.  unless i 
>misunderstand what you're saying here, Fred.
>
>one of the purposes of coding is to minimize the transmission bandwidth 
>of a signal.

That's "source coding", or compression.

>  another purpose of coding is to put in enough redundancy 
>that the receiver can detect and correct some data errors.

That's "channel coding", or error control coding or error correction
coding.


>  that, of 
>course increases bandwidth, but when combined with the coding that 
>decreases bandwidth, most of the time we get *both* error correction 
>*and* decreased transmission bandwidth.

That would be joint source-channel coding, which nobody has ever
really figured out how to do broadly or efficiently.   Nearly
universally the compression is done separately from the error
correction.

>
>perhaps i just dunno what you intended to say.

I think Fred was talking about channel coding.

>
>
>-- 
>
>r b-j                  rbj@audioimagination.com
>
>"Imagination is more important than knowledge."
>
>

Eric Jacobsen
Anchor Hill Communications
www.anchorhill.com

Thank you all for the answer.

I seem to have created confusion by using transfer. Let me clarify.
Transmission of data is not of primary concern. But storing the data in
frequency domain seem to provide advantage.

I have multiple data sources. Assume each is generated at different rates.
In a pure digital world where I already have data available, this just
means picking up the data at the right rate.

Theoritically, I can pick up data from each source at different rate and
then convert them into frequency domain and combine them.

Now I can combine these data source and store them.

Since each source is at a different rate, I should be able to extract data
by using filter. The advantage is that by combining data into frequency
domain, I am hopefully using less bits to store same amount of data that
would take more bits if I were to store directly in time domain.

I can transmit the same data effectively reducing the bandwidth requirement
to transfer the data. All this at a increased processing complexity.

Does this make sense?

manishp <58525@dsprelated> wrote:

(snip)
> I seem to have created confusion by using transfer. Let me clarify.
> Transmission of data is not of primary concern. But storing the data in
> frequency domain seem to provide advantage.

Pretty much the same, though in actual practice it might be
slightly different. For one example where it is different, 
the analog TV luminance signal is AM broadcast, but FM on
video tape. It is too hard to store the large frequency range
(from close to zero up to 4MHz or so) on magnetic tape.

> I have multiple data sources. Assume each is generated at different rates.
> In a pure digital world where I already have data available, this just
> means picking up the data at the right rate.

How many, and at what rate. It can be done, but it is much easier
to combine the digital signals, and then use a convenient digital
modulation method. The ATSC ( US broadcast digital television)
system can put between one and about five (maybe more) digital
TV streams into one channel. 

The N/2, N/4, N/8, etc, division is especially easy. In the
digital stream, even bits belong to the first, odd bits that
are even after dividing by two (and ignoring the remainder 1)
to the second, even after dividing by four to the third stream, etc.

> Theoritically, I can pick up data from each source at different 
> rate and then convert them into frequency domain and combine them.

The description sounds like converting each to an analog signal
in some way, then shifting them into different frequency bands.
(Or generating them directly in different bands) then combining them.

I could also imagine generating a digitized signal representing
the sum of the different modulated signals, then putting that
combined signal through a DAC. I presume some are doing something
like that now, though I don't know any examples.

It shouldn't be so hard to take two digitized stereo channels
and generate the appropriate multiplexed signal for FM
transmission. Then a little more work to take that digital
signal and generate an FM signal at a 10.7MHz IF. I presume
that there are DACs fast enough to generate directly an FM RF
signal ready to transmit.

> Now I can combine these data source and store them.

In the usual systems, you need some guard band to keep them
from interfering. Some can stand some overlap, but likely
less efficient in bandwidth for the bit rate. 

> Since each source is at a different rate, I should be able to extract data
> by using filter. The advantage is that by combining data into frequency
> domain, I am hopefully using less bits to store same amount of data that
> would take more bits if I were to store directly in time domain.

It depends on what you mean by storing bits directly. The early 
digital storage systems weren't very efficient in media use, but
were easier to build the required hardware for. As electronics
got cheaper, the dividing line moved, and fancier recording
systems became available.

> I can transmit the same data effectively reducing the 
> bandwidth requirement to transfer the data. 
> All this at a increased processing complexity.

Well, if it is increasing analog electronics complexity,
then probably not effective. 

> Does this make sense?

-- glen