# Analog modulation

Started by 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.

Jerry
--
Engineering is the art of making what you want from things you can get.
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```
```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
>

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?

--
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:

> > 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:
>
>
>>
>>>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:
>>
>>
>>>
>>>> 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
```