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Analog modulation

Started by Vladimir Vassilevsky January 13, 2006
Given an analog bandlimited signal, is it possible to create a 
continuous time reversible procedure to reduce the bandwidth without 
losses? In the other words, is it possible to create a bandwidth 
reducing analog modulation?

Looks like the answer is no, however I can't make a mathematical proof 
of this.

VLV

Vladimir Vassilevsky wrote:
> Given an analog bandlimited signal, is it possible to create a > continuous time reversible procedure to reduce the bandwidth without > losses?
If the signal is f(t) and bandlimited in the interval (-B, B), then the signal g(t) := f(a t) is bandlimited to (-a B, a B). In other words, you can scale f to have arbitrary small bandwidth. The inverse is simply f(t) = g(t/a).
> In the other words, is it possible to create a bandwidth > reducing analog modulation?
The above scaling process can be achieved by sampling the bandlimited signal and reconstructing with another sampling rate. Does that count as analog modulation (input and output are analog signals)?
> Looks like the answer is no, however I can't make a mathematical proof > of this.
I don't think you'll find one. Regards, Andor

Andor wrote:


>>In the other words, is it possible to create a bandwidth >>reducing analog modulation? > > > The above scaling process can be achieved by sampling the bandlimited > signal and reconstructing with another sampling rate. Does that count > as analog modulation (input and output are analog signals)?
This does not count. It is possible to suggest many bandwidth reduction methods making use of some kind of sampling. The question is if there could be a continuos process to do that.
>>Looks like the answer is no, however I can't make a mathematical proof >>of this. > > I don't think you'll find one. >
VLV
Vladimir Vassilevsky wrote:
> Andor wrote: > > > >>In the other words, is it possible to create a bandwidth > >>reducing analog modulation? > > > > > > The above scaling process can be achieved by sampling the bandlimited > > signal and reconstructing with another sampling rate. Does that count > > as analog modulation (input and output are analog signals)? > > This does not count. It is possible to suggest many bandwidth reduction > methods making use of some kind of sampling. The question is if there > could be a continuos process to do that.
Define "continuous process".
Vladimir Vassilevsky wrote:
> > Given an analog bandlimited signal, is it possible to create a > continuous time reversible procedure to reduce the bandwidth without > losses? In the other words, is it possible to create a bandwidth > reducing analog modulation? > > Looks like the answer is no, however I can't make a mathematical proof > of this.
How can you discard bandwidth without discarding something? Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Vladimir Vassilevsky wrote:
> > Given an analog bandlimited signal, is it possible to create a > continuous time reversible procedure to reduce the bandwidth without > losses? In the other words, is it possible to create a bandwidth > reducing analog modulation? > > Looks like the answer is no, however I can't make a mathematical proof > of this. > > VLV >
Vladimir, You can of remove most of one sideband from the AM signal to give Vestigial Sideband modulation, or remove all of one sideband and the carrier to give Single Sideband Suppressed Carrier modulation. I can't think of anything else, but if there is, you could make a lot of money out of it (:=) Regards, John
On Fri, 13 Jan 2006 19:51:41 +0000, Vladimir Vassilevsky wrote:

> > Given an analog bandlimited signal, is it possible to create a > continuous time reversible procedure to reduce the bandwidth without > losses? In the other words, is it possible to create a bandwidth > reducing analog modulation? > > Looks like the answer is no, however I can't make a mathematical proof > of this. >
Given an analog signal, you want to manipulate the frequencies in such a way as to reduce the bandwidth of the signal, but then have the modified stream have the same information content (so the mapping is reversible). Is this right? How about slowing it down? -- Regards, Bob Monsen "I cannot persuade myself that a beneficent and omnipotent God would have designedly created parasitic wasps with the express intention of their feeding within the living bodies of Caterpillars" -- Charles Darwin
Andor wrote:

> Vladimir Vassilevsky wrote: > > Andor wrote: > > > > > > >>In the other words, is it possible to create a bandwidth > > >>reducing analog modulation? > > > > > > > > > The above scaling process can be achieved by sampling the bandlimited > > > signal and reconstructing with another sampling rate. Does that count > > > as analog modulation (input and output are analog signals)? > > > > This does not count. It is possible to suggest many bandwidth reduction > > methods making use of some kind of sampling. The question is if there > > could be a continuos process to do that. > > Define "continuous process".
Is recording onto a recorder and playing back at a different speed a "continuous process"? How does it make a difference if the recorder is analog or digital?
Andor said the following on 14/01/2006 11:38:
> Andor wrote: > > >>Vladimir Vassilevsky wrote: >> >>>Andor wrote: >>> >>> >>> >>>>>In the other words, is it possible to create a bandwidth >>>>>reducing analog modulation? >>>> >>>> >>>>The above scaling process can be achieved by sampling the bandlimited >>>>signal and reconstructing with another sampling rate. Does that count >>>>as analog modulation (input and output are analog signals)? >>> >>>This does not count. It is possible to suggest many bandwidth reduction >>>methods making use of some kind of sampling. The question is if there >>>could be a continuos process to do that. >> >>Define "continuous process". > > > Is recording onto a recorder and playing back at a different speed a > "continuous process"? How does it make a difference if the recorder is > analog or digital?
Playing back at a faster speed is non-causal, and so not much use for real-time processes, I guess. -- Oli
Oli Filth said the following on 14/01/2006 13:12:
> Andor said the following on 14/01/2006 11:38: > >> Andor wrote: >> >> >>> Vladimir Vassilevsky wrote: >>> >>>> Andor wrote: >>>> >>>>> The above scaling process can be achieved by sampling the bandlimited >>>>> signal and reconstructing with another sampling rate. Does that count >>>>> as analog modulation (input and output are analog signals)? >>>> >>>> >>>> This does not count. It is possible to suggest many bandwidth reduction >>>> methods making use of some kind of sampling. The question is if there >>>> could be a continuos process to do that. >>> >>> >>> Define "continuous process". >> >> Is recording onto a recorder and playing back at a different speed a >> "continuous process"? How does it make a difference if the recorder is >> analog or digital? > > > > Playing back at a faster speed is non-causal, and so not much use for > real-time processes, I guess. >
Although, I'm an idiot - you'd be playing back slower to reduce the bandwidth... However, that would instead take an infinite amount of memory for a real-time process. -- Oli