Frequencies and muxing

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Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
92
Hello,

For any engineers here: I’m looking for a mathematical, non-philosophical, directly engineering-grade answer to the following question:

We can take hundreds of independent conversations and modulate them on separate analog frequencies, combine those modulated frequencies into one aggregate frequency, which we can then send down a coax wire, where it can be demuxed back into the individual components.

I want to know mathematically how the resulting wave is retaining the modulated data on each frequency, with all of their associated overtones, timbres, kept discrete despite being “flattened” into one parent wave. I understand we can filter and access the frequencies, but my question is with the retention of data within them after having aggregated them into one.

This is not a trolling question, and it’s specifically for research I’m carrying out on a model for human reason.

I’m perfectly content with, “There is currently no scientific explanation for this phenomenon.”

Thanks for any help!

JS
 

andrewmm

Joined Feb 25, 2011
1,470
HI,

we are engineers, we can not as far as I know delve into "human reason" as you ask.

If you want to ask the pure engineering question , without the human reasoning part of the question.
then please can I suggest that you repost.
 

Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
92
HI,

we are engineers, we can not as far as I know delve into "human reason" as you ask.

If you want to ask the pure engineering question , without the human reasoning part of the question.
then please can I suggest that you repost.
Hey, I’m not looking for the human reason component. I simply said that’s what the question is ultimately about, and not a “trolling” question. I only want the specific mathematics, if available, that describes the modulated data retention in a wave aggregation.
 

andrewmm

Joined Feb 25, 2011
1,470
Re the Frequency and muxing question,

Purely mathematically

Can we agree that by using the word frequency , we are talking about a time variable signal ?
after all, frequency is "cycles per second"

So any instantaneous point in time can not tell you anything about a frequency .

So if we agree the above,
lets define a signal as varying in amplitude over time.,

theory one.
Any signal, can be made up by adding a number of single frequencies, which are phase / amplitude modulated.
This can be shown with sine waves or walsh codes et all ( there are many ways )

theory two
Any signal we wish to send over a cable is band limited,

theory three, Take a sine wave for simplicity, but it works for square waves et all,
Any frequency at frequency A, does not interfere with a separate and different frequency at frequency b.


So simple mind experiment,

Take a frequency of 1 Hz, and another at 3 Hz,

In the frequency domain they are two, distinct signals,
in the time domain, they will appear as a "partly squared off " wave

But the individual frequencies are stil there,
At its simplest, all thats needed is to filter out the one you dont want.

For reference, if you add , 1Hz, 3 Hz, 5 Hz, 7 Hz, 9 Hz,

In the frequency domain , they will be independent frequencies ( see theory three )
In the time domain , they will look like a square wave

https://en.wikipedia.org/wiki/Square_wave


and a bit more maths here

https://en.wikipedia.org/wiki/Fourier_transform

Nothing on " human reasoning "
 

crutschow

Joined Mar 14, 2008
27,213
The mathematics of multiplexing is quite clear and complete, showing how all the original frequencies can be recovered.
You seem to be asking a philosophical question, not an engineering one.
 

Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
92
Re the Frequency and muxing question,

Purely mathematically

Can we agree that by using the word frequency , we are talking about a time variable signal ?
after all, frequency is "cycles per second"

So any instantaneous point in time can not tell you anything about a frequency .

So if we agree the above,
lets define a signal as varying in amplitude over time.,

theory one.
Any signal, can be made up by adding a number of single frequencies, which are phase / amplitude modulated.
This can be shown with sine waves or walsh codes et all ( there are many ways )

theory two
Any signal we wish to send over a cable is band limited,

theory three, Take a sine wave for simplicity, but it works for square waves et all,
Any frequency at frequency A, does not interfere with a separate and different frequency at frequency b.


So simple mind experiment,

Take a frequency of 1 Hz, and another at 3 Hz,

In the frequency domain they are two, distinct signals,
in the time domain, they will appear as a "partly squared off " wave

But the individual frequencies are stil there,
At its simplest, all thats needed is to filter out the one you dont want.

For reference, if you add , 1Hz, 3 Hz, 5 Hz, 7 Hz, 9 Hz,

In the frequency domain , they will be independent frequencies ( see theory three )
In the time domain , they will look like a square wave

https://en.wikipedia.org/wiki/Square_wave


and a bit more maths here

https://en.wikipedia.org/wiki/Fourier_transform

Nothing on " human reasoning "
thanks for the reply again. :)

You’ve thoroughly described how we can get at those subcarrier frequencies, but the *modulated data* thereof is the question. If we have a single waveform that represents 900 simultaneous conversations, each on a different modulated subcarrier frequency, we can filter for those individual subcarrier frequencies themselves to be recovered irrespective of the modulated data they carry. But I’m not seeing any math that describes how the altered subcarriers combine and retain discrete, lossless data and addressability post aggregation. Over 1 second cross-section of the wave, we have fourier components that describe the signal. What is the explanation for the subcarriers remaining 100% distinct with concurrent nested data post modulation and aggregation?
 

andrewmm

Joined Feb 25, 2011
1,470
See my reply above.
which part of the maths as shown in the wiki are you having problems with ?

Ok, lets take this one step at a time, no big jumps.

Do we agree that a frequency is a signal varying in amplitude over time ?


The three theories

lets take one


Any signal, can be made up by adding a number of single frequencies, which are phase / amplitude modulated.
This can be shown with sine waves or walsh codes et all ( there are many ways )


Do you agree that this is a truth ?

( note edited )
 

Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
92
which part of the maths as shown in the wiki are you having problems with ?

Ok, lets tka e this one step at a time, nobig jumps.

The three theories

lets take one


Any signal, can be made up by adding a number of single frequencies, which are phase / amplitude modulated.
This can be shown with sine waves or walsh codes et all ( there are many ways )


Do you agree that this is a truth ?
100%
 

andrewmm

Joined Feb 25, 2011
1,470
Sorry this is going to be slow, but we can try.

Do we agree that an amplitude varying over time is a signal ?

Think of a simple sine wave, draw it out.
 

MrChips

Joined Oct 2, 2009
23,528
I’m perfectly content with, “There is currently no scientific explanation for this phenomenon.”

Thanks for any help!

JS
You do not need to go there. There is a perfect mathematical explanation.

You asked this question before and we gave you the mathematical answer which you refused to accept. For this reason your thread was locked.

Why are you asking the same question?
This thread will reach the same fate as the previous thread... soon.
 

Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
92
This is a screen shot from the software Melodyne:

7567406C-53DA-4300-A516-593C7F87D3E1.jpeg

If the original wave was a real piano recorded by a microphone, the aggregate wave can be parsed into their individual frequencies using Fourier transforming, with intervalic overtones intact.

Now, let’s say instead of just a piano, 900 different instruments were recorded by the single mic. The mic sees “one wave.” A filter can recover groups of frequencies, but 900 are crosstalking all over the place. How are 900 different isolated instruments recoverable with all data isolated and intact?
That’s what’s happening in the coax/conversation original example. We’ve modulated 900 subcarrier frequencies to carry the conversation, but they are losslessly intact with no crosstalk. Where’s the “metadata“ that describes the non-interfering grouping and nesting?
 

bogosort

Joined Sep 24, 2011
674
If we have a single waveform that represents 900 simultaneous conversations, each on a different modulated subcarrier frequency, we can filter for those individual subcarrier frequencies themselves to be recovered irrespective of the modulated data they carry. But I’m not seeing any math that describes how the altered subcarriers combine and retain discrete, lossless data and addressability post aggregation. Over 1 second cross-section of the wave, we have fourier components that describe the signal. What is the explanation for the subcarriers remaining 100% distinct with concurrent nested data post modulation and aggregation?
The reason this works is because of the defining characteristic of waves, i.e., the physical property of waves to combine in linear superposition. That is, when two or more waveforms combine, they interfere with each other constructively and destructively to create a new waveform. Because this process is linear, the component waveforms retain their individual properties (except in the degenerate case of perfect cancellation).

As a simple analogy, bricks have a similar property, though they only combine constructively. If we build a house with bricks, each individual brick retains its properties in the combination (the house). Mathematically, we say that combining bricks is an arithmetic sum (always constructive interference), whereas combining waves is an algebraic sum (constructive and destructive interference).

There's nothing surprising about bricks retaining their "information" in the construction of a house, right? It's the same principle with waves, but since waves can interfere destructively, the resulting "house" doesn't like much like the individual components. But there's nothing spooky going on -- just arithmetic with positive and negative values instead of just positive values.
 

Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
92
You do not need to go there. There is a perfect mathematical explanation.

You asked this question before and we gave you the mathematical answer which you refused to accept. For this reason your thread was locked.

Why are you asking the same question?
This thread will reach the same fate as the previous thread... soon.
The existing fourier filtration math is not the question. It is the lossless isolation of 900 grouped, discrete timbres on what amounts to a “polyphonic” signal. The monophonic makes 100% sense. The equipment can be built to get at the subcarriers. I want to know the mechanism of why the subcarriers are retaining all of the associated grouped waves losslessly post aggregation.
 

Thread Starter

Jennifer Solomon

Joined Mar 20, 2017
92
You do not need to go there. There is a perfect mathematical explanation.

You asked this question before and we gave you the mathematical answer which you refused to accept. For this reason your thread was locked.

Why are you asking the same question?
This thread will reach the same fate as the previous thread... soon.
The thread was not locked for that reason. The thread was locked because we went into a different topic, and people were complaining due to that (good) reason. This is not going off topic, and this is a similar, but different question.
 

bogosort

Joined Sep 24, 2011
674
Now, let’s say instead of just a piano, 900 different instruments were recorded by the single mic. The mic sees “one wave.” A filter can recover groups of frequencies, but 900 are crosstalking all over the place. How are 900 different isolated instruments recoverable with all data isolated and intact?
They're not. If the frequency components of the 900 different instruments are interfering (mixing) with each other, then we will never be able to perfectly recover the individual instruments. This is why multiplexing systems must separate the bandwidths of each channel -- if two channels shared the same bandwidth, we'd have no way of knowing which part belonged to which.
 

MrChips

Joined Oct 2, 2009
23,528
There is no "metadata".

Take two sine waves sin(a) and sin(b). Now try to add them together. Assuming that the addition is perfect (which is never the case), the result is:

sin(a) + sin(b) = 2sin((a+b)/2) cos((a-b)/2)

Now you have four frequencies in the mix:
a
b
(a+b)/2
(a-b)/2

I alluded to the fact that no addition is perfect. One has to take into account inter-modulation distortion which will introduce cross products.

It is all in the mathematics.
 

bogosort

Joined Sep 24, 2011
674
I alluded to the fact that no addition is perfect. One has to take into account inter-modulation distortion which will introduce cross products.
This is false for linear systems. Only nonlinear systems will produce intermodulation distortion. The linear sum of multiple of sine waves (or any other waveform) is indeed perfect.

It is all in the mathematics.
It's all in the physics; the math is a model.
 
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