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Is Digital Audio Transmission Analog? [video]

pkane

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Aha!
But isn't Fourier analysis an approximation? After all, sine wave components approximate a square wave, but never actually make it.
Staying with mathematics, a perfect square wave does exist, but a composition of sine waves keeps getting closer and closer to a perfect square wave, and indeed one needs an infinite number of them.
Using switches (transistor, relays or even a push button) to create a square wave, one starts with DC , where are the sine wave components?
There aren't any!
Now if you filter that, you create the sine waves, just like my glass example.

There is no perfect square wave in nature, no matter how it's generated. All signals are bandwidth limited, and discrete Fourier transform can represent any signal, including any bandwidth-limited square wave perfectly (not as an approximation) as long as it's sampled at twice the bandwidth rate -- Shannon, Nyquist, Whittaker, Kotelnikov, Gabor, et al.

Sine wave components are all there, no matter how the square wave is generated. It's like asking where are the inches if a length is measured in centimeters. They are both there, it's just a different representation of the same thing.
 

Ken Tajalli

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There is no perfect square wave in nature, no matter how it's generated.
All signals are bandwidth limited,
I accept that.
and discrete Fourier transform can represent any signal, including any bandwidth-limited square wave perfectly (not as an approximation) as long as it's sampled at twice the bandwidth rate -- Shannon, Nyquist, Whittaker, Kotelnikov, Gabor, et al.
You just left nature! you moved back into theory. How would you naturally create a band limited square wave using sine waves? how many components are needed? will it ever be practically perfect duplicate?
Remember Sampling, Shannon etc, are all mathematical.
Sine wave components are all there, no matter how the square wave is generated. It's like asking where are the inches if a length is measured in centimeters. They are both there, it's just a different representation of the same thing.
No, it is like saying a big slap of Marble is actually made up of tiny marble tiles, because I could make one such thing.
Maybe you could, but in practice it is far far easier to just make a slab of marble than make microscopic marble tiles and stick them together.
I am not saying Fourier was wrong, or not understand what you are saying.
Expanding the scope of the argument can also change the outcome of the argument.
This thread started to question, within the scope of Audio in a hifi system - if the Digital audio transmission through a conductor, Analogue or not?
If you put your microscope on anything, you can argue there are no tables, glass water or anything! it is all molecules and atoms .....
But in a practical natural world, that ain't so.
Digital audio (within the hifi world) is generated (if electrically) by switching devices (transistors). There are no sine waves. The band limiting creates distortions , slows the rise/fall time. These distortions or deformities can be imagined mathematically to be composed of unlimited sine waves.
In reality, they are caused by capacitances, inductances etc.
 
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Plcamp

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Maybe this will convince you the the analogue waveform and the Fourier breakdown are inextricable the same thing?

The video has four parts where you can see the multiple sinusoids and the resulting waveform are just representations of exactly the same thing. Using a mechanical machine.

 

Ken Tajalli

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Maybe this will convince you the the analogue waveform and the Fourier breakdown are inextricable the same thing?
Thanx, I am somewhat versed in Fourier analysis.
But the machine is fascinating!

Edit
I just watched all four. My chin is to the floor!
What a genius.
Once again, thanx for the videao.
 
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pkane

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You just left nature! you moved back into theory. How would you naturally create a band limited square wave using sine waves? how many components are needed? will it ever be practically perfect duplicate?

Again, it doesn't matter how a square wave is generated -- it always consists of a finite number of odd harmonics. How many components are needed is determined by bandwidth. I generate band-limited square waves in Multitone all the time.

No, it is like saying a big slap of Marble is actually made up of tiny marble tiles, because I could make one such thing.
No. It is an equivalent and exact representation using a mathematical transformation, just like inches can always be converted to centimeters (yes, using math).

You're confusing what's easier for you to generate with what actually is.
 

DonH56

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Can't believe this is still going... I cannot recall ever trying to create a square wave by summing sine waves except as a mathematical exercise (but admit I have done that fairly often as it is a nice way to show what comprises a square wave). A switch (between two levels) or clamp (diodes or otherwise, overdriven by a sine wave) is the usual "analog" way, a DAC will generate it directly by switching between two specified levels. The result is not (ever) a "perfect" square wave but can get pretty close. The square wave that results will, when analyzed using Fourier, show tones in the usual odd progression decreasing as 1/N for N = 1, 3, 5, 7,... just like the theory shows. A real "square wave" will have additional even-order components, and the odd components may not be "perfect", since you can't generate an ideal square wave in the real world (the edges are not perfectly sharp). That does not invalidate Fourier analysis. Make a square wave however you like, then use Fourier to analyze the frequencies comprising it. Or a sine wave, triangle wave, or anything else. That is one way of determining the "goodness" of a square (or any) wave, do Fourier and see how many "other" frequencies than the ideal ones you expect are in there.

For example, an ideal triangle wave is discontinuous at the top and bottom, but in the real world those sharp peaks will be rounded off because it does not have infinite bandwidth, and Fourier analysis will show that. (A triangle wave is mathematically the integral of a square wave, and in practice that is one way to create one, others being things like a switch and a current source or two into a capacitor.) Similarly, a real sine wave will not be a single tone but have (hopefully) small other frequencies present, because creating a "perfect" sine wave is impractical (again we can get awfully close!)

As mentioned above, for real-world calculations the Fourier series will be limited, but in practice it rarely matters a you can get "close enough". If sampled, you need a long enough record to capture the "flat-top" behavior (you will get the DC term regardless) and enough time resolution to capture the edges (usual Nyquist criteria for a sampled system, >2x the highest frequency). For a DAC that means twice the bandwidth of the output anti-imaging filter, which suppresses higher frequencies in normal operation, so there is no need for "infinite" bandwidth because the real signal is not that wideband. At the other end (low frequencies), at 44.1 kS/s just 44,100 samples is 1 second's worth of data to capture down to 1 Hz, and FFTs are routinely a million points or so in test systems to capture sub-Hz signals.

Whatever - Don
 

Ken Tajalli

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Can't believe this is still going... I cannot recall ever trying to create a square wave by summing sine waves except as a mathematical exercise (but admit I have done that fairly often as it is a nice way to show what comprises a square wave). A switch (between two levels) or clamp (diodes or otherwise, overdriven by a sine wave) is the usual "analog" way, a DAC will generate it directly by switching between two specified levels. The result is not (ever) a "perfect" square wave but can get pretty close. The square wave that results will, when analyzed using Fourier, show tones in the usual odd progression decreasing as 1/N for N = 1, 3, 5, 7,... just like the theory shows. A real "square wave" will have additional even-order components, and the odd components may not be "perfect", since you can't generate an ideal square wave in the real world (the edges are not perfectly sharp). That does not invalidate Fourier analysis. Make a square wave however you like, then use Fourier to analyze the frequencies comprising it. Or a sine wave, triangle wave, or anything else. That is one way of determining the "goodness" of a square (or any) wave, do Fourier and see how many "other" frequencies than the ideal ones you expect are in there.

For example, an ideal triangle wave is discontinuous at the top and bottom, but in the real world those sharp peaks will be rounded off because it does not have infinite bandwidth, and Fourier analysis will show that. (A triangle wave is mathematically the integral of a square wave, and in practice that is one way to create one, others being things like a switch and a current source or two into a capacitor.) Similarly, a real sine wave will not be a single tone but have (hopefully) small other frequencies present, because creating a "perfect" sine wave is impractical (again we can get awfully close!)

As mentioned above, for real-world calculations the Fourier series will be limited, but in practice it rarely matters a you can get "close enough". If sampled, you need a long enough record to capture the "flat-top" behavior (you will get the DC term regardless) and enough time resolution to capture the edges (usual Nyquist criteria for a sampled system, >2x the highest frequency). For a DAC that means twice the bandwidth of the output anti-imaging filter, which suppresses higher frequencies in normal operation, so there is no need for "infinite" bandwidth because the real signal is not that wideband. At the other end (low frequencies), at 44.1 kS/s just 44,100 samples is 1 second's worth of data to capture down to 1 Hz, and FFTs are routinely a million points or so in test systems to capture sub-Hz signals.

Whatever - Don
See how easy it is to get drawn in!
All it takes is enough free time and an argumentative nature :).
Being bored can help too.
 

pablolie

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The thing that analog transmission is far from perfect, in fact it is very flawed. Degradation of analog signals is in their very nature - the question is just how bad it is. Digital allows you to decouple/protect payload integrity from any signal integrity considerations. Claiming an analog signal is the ideal is actually ridiculous if you understand analog technologies - analog is actually the trickiest, most treacherous parts in circuit design. Digital is safe.
 

pkane

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See how easy it is to get drawn in!
All it takes is enough free time and an argumentative nature :).
Being bored can help too.

I start out with an implicit assumption that those posting questions here are genuinely seeking an answer and are not here to argue. But I'm often proven wrong ;)
 

Ken Tajalli

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I start out with an implicit assumption that those posting questions here are genuinely seeking an answer and are not here to argue. But I'm often proven wrong ;)
Well ...
There was no question!
As knowledgeable as you are (respect), it was just a discussion on finer points of the nature of the matter.

Tell me, if you didn't have the time, or didn't care to argue your own point, would you have dropped in here to respond to me?
Me? Business is slow today .. . . .:( :)
 

pkane

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Tell me, if you didn't have the time, or didn't care to argue your own point, would you have dropped in here to respond to me?
Me? Business is slow today .. . . .:( :)

Of course. You quoted me in your post, and asked me a follow-up question. It would be rude not to answer.
 

tmtomh

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No, it is like saying a big slap of Marble is actually made up of tiny marble tiles, because I could make one such thing.

Two possibilities:

1. Human scientific and mathematical knowledge on this point is wrong;
2. Your common-sense intuition that makes a slab of marble seem like an apt analogy here is wrong.

I'm confident others can come to their own conclusion about which of these two possibilities is more likely.
 

Blumlein 88

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Some natural square waves.
1670000169758.png
 

Ken Tajalli

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Two possibilities:

1. Human scientific and mathematical knowledge on this point is wrong;
2. Your common-sense intuition that makes a slab of marble seem like an apt analogy here is wrong.

I'm confident others can come to their own conclusion about which of these two possibilities is more likely.
Only two?
You mean one, that I am wrong!
Science and Maths can not be wrong, that's a given - and my analogy is . . . well wrong!
As I said, it is a question of scale/scope or environment.
A slab of marble is not made from tiny pieces of marble that can be felt or seen (scale) or matter as a kitchen worktop (environment) - BUT - in a lab, under a microscope, it can indeed be broken down to tiny pieces of marble.
Similarly, (as an example) a sequential switching of DC current (square wave) into a strobe light does not contain sine waves!
Of course, one can connect an analyser to the current pulses and see some sine wave components - but who cares? The strobe light doesn't.
You want it in digital audio transmission?
The digital signal within a conductor, for as long as the eye does not completely close and the receiver can determine the zeros from ones , does not include any sine waves, and if it does, who cares? the receiver doesn't.
Up to the point (scale) that data can not be read.
 

Blumlein 88

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Only two?
You mean one, that I am wrong!
Science and Maths can not be wrong, that's a given - and my analogy is . . . well wrong!
As I said, it is a question of scale/scope or environment.
A slab of marble is not made from tiny pieces of marble that can be felt or seen (scale) or matter as a kitchen worktop (environment) - BUT - in a lab, under a microscope, it can indeed be broken down to tiny pieces of marble.
Similarly, (as an example) a sequential switching of DC current (square wave) into a strobe light does not contain sine waves!
Of course, one can connect an analyser to the current pulses and see some sine wave components - but who cares? The strobe light doesn't.
You want it in digital audio transmission?
The digital signal within a conductor, for as long as the eye does not completely close and the receiver can determine the zeros from ones , does not include any sine waves, and if it does, who cares? the receiver doesn't.
Up to the point (scale) that data can not be read.
If you switch your DC current to your light very fast, a DC voltmeter will read nothing, because it is not DC. You still have waves with frequency even if derived from a DC source you manipulate. I fail to see what point you are getting at here.
 

Ken Tajalli

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If you switch your DC current to your light very fast, a DC voltmeter will read nothing, because it is not DC. You still have waves with frequency even if derived from a DC source you manipulate. I fail to see what point you are getting at here.
Horses for courses.
For as long as the strobe works, all else is irrelevant.
If your voltmeter can not read it, it is not up to the task, use a fast scope to see the pulses,
My point is that we are deliberately breaking down a square wave into sine wave components, but to the strobe light it is irrelevant.
Do you include a Fourier analysis for your car indicator lights? Surely there are rise time issues and RF noise on the cables.
The strobe light does not require sine waves or care about them.
But surely if the DC supply is not up to the task, or the cable used gets so long as to interfere, then, and only then it becomes an issue.
Under certain conditions a square wave acts/is a combination of sine waves, under certain conditions it is just a square wave.
 
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Atanasi

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If your voltmeter can not read it, it is not up to the task, use a fast scope to see the pulses
If the voltmeter doesn't detect the pulses, it means there is a frequency of pulses that is too large. That is the bandwidth limit of the meter.
DC switches cannot switch current immediately, either. Inductance and capacitance mean that the current and the voltage take some time to settle, so there is a maximum frequency. DC switches also have a bandwidth limit.
 

Ken Tajalli

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If the voltmeter doesn't detect the pulses, it means there is a frequency of pulses that is too large. That is the bandwidth limit of the meter.
DC switches cannot switch current immediately, either. Inductance and capacitance mean that the current and the voltage take some time to settle, so there is a maximum frequency. DC switches also have a bandwidth limit.
Does a car indicator system, care about any of this?
Is it affected by any of this?
Does the band limiting, Fourier analysis, rise time, RF noise etc. have any meaning or effects to a car indicator system?
After all it works on square waves!
 
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