question about non-uniform sampling?

Ron N. wrote:

   ...

>>I'd be happy to wait a whole week for a filter to compose the last
>>movement of Beethoven's Ninth, given only the the first three. Think how
>>much work (and time!) such a filter would have saved Beethoven himself!
> 
> 
> How would the filter have saved any work?  If fed a last movement
> of silence, that's what would be reproduced, given a few billion bits
> of precision per sample and a lowpass filter an equivalent number
> of dB down in the stop band.
> 
> What you think is the first sample of the first movement, can't be
> correctly bandlimited to the precision required unless the low pass
> filter is fed the last sample of the last movement.

The hypothesis is that the first three movements were oversampled, using 
enough samples to suffice for all four. According to Carlos, it doesn't 
matter where the samples are just so long as there are enough of them. 
We can deduce from Carlos's claim that the entire symphony was sampled. 
If the claim is valid, then the entire symphony can be reconstructed. I 
don't suppose that the entire symphony including the choral movement can 
be reconstructed from the samples. My intent is /reductio ad absurdam/.

Carlos and I understand the argument, but see it from different vantages.

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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glen herrmannsfeldt wrote:
> Jerry Avins wrote:
> 
> (snip)
> 
>> I'd be happy to wait a whole week for a filter to compose the last 
>> movement of Beethoven's Ninth, given only the the first three. Think 
>> how much work (and time!) such a filter would have saved Beethoven 
>> himself!
> 
> 
> Given all the samples of his work and the first three as input, one 
> might compute in some weeks the most probable fourth movement.

Including the choral parts, which were unprecedented for a Beethoven 
symphony?

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

cs_posting@hotmail.com wrote:
> Ron N. wrote:
>
> > What you think is the first sample of the first movement, can't be
> > correctly bandlimited to the precision required unless the low pass
> > filter is fed the last sample of the last movement.
>
> There is no such thing as a bandlimited sample.  A sample is a scaled
> impulse, and an impulse is by definition for all frequencies.

Err... correct.  I should have said a sample of a sufficiently
bandlimited signal, where the pre-sampling low-pass filter
would presumably need support from at least the duration
of the entire symphony in order to produce it from a local
group of subsamples, in theory of course.

The thought experiment I was visualizing was using a very
wide FIR filter on an infinite width of sufficiently dense and
precise samples to do the proper bandlimiting.  ( It's been too
long since I've soldered any analog filter components :)


IMHO. YMMV.
-- 
rhn A.T nicholson d.O.t C-o-M

cs_posting@hotmail.com wrote:
> Ron N. wrote:
>
> > What you think is the first sample of the first movement, can't be
> > correctly bandlimited to the precision required unless the low pass
> > filter is fed the last sample of the last movement.
>
> There is no such thing as a bandlimited sample.  A sample is a scaled
> impulse, and an impulse is by definition for all frequencies.

Err... correct.  I should have said a sample of a sufficiently
bandlimited signal, where the pre-sampling low-pass filter
would presumably need support from at least the duration
of the entire symphony in order to produce it from a local
group of subsamples, in theory of course.

The thought experiment I was visualizing was using a very
wide FIR filter on an infinite width of sufficiently dense and
precise samples to do the proper bandlimiting.  ( It's been too
long since I've soldered any analog filter components :)


IMHO. YMMV.
-- 
rhn A.T nicholson d.O.t C-o-M

cs_posting@hotmail.com wrote:
> Ron N. wrote:
>
> > What you think is the first sample of the first movement, can't be
> > correctly bandlimited to the precision required unless the low pass
> > filter is fed the last sample of the last movement.
>
> There is no such thing as a bandlimited sample.  A sample is a scaled
> impulse, and an impulse is by definition for all frequencies.

Err... correct.  I should have said a sample of a sufficiently
bandlimited signal, where the pre-sampling low-pass filter
would presumably need support from at least the duration
of the entire symphony in order to produce it from a local
group of subsamples, in theory of course.

The thought experiment I was visualizing was using a very
wide FIR filter on an infinite width of sufficiently dense and
precise samples to do the proper bandlimiting.  ( It's been too
long since I've soldered any analog filter components :)


IMHO. YMMV.
-- 
rhn A.T nicholson d.O.t C-o-M

cs_posting@hotmail.com wrote:
> Ron N. wrote:
>
> > What you think is the first sample of the first movement, can't be
> > correctly bandlimited to the precision required unless the low pass
> > filter is fed the last sample of the last movement.
>
> There is no such thing as a bandlimited sample.  A sample is a scaled
> impulse, and an impulse is by definition for all frequencies.

Err... correct.  I should have said a sample of a sufficiently
bandlimited signal, where the pre-sampling low-pass filter
would presumably need support from at least the duration
of the entire symphony in order to produce it from a local
group of subsamples, in theory of course.

The thought experiment I was visualizing was using a very
wide FIR filter on an infinite width of sufficiently dense and
precise samples to do the proper bandlimiting.  ( It's been too
long since I've soldered any analog filter components :)


IMHO. YMMV.
-- 
rhn A.T nicholson d.O.t C-o-M

cs_posting@hotmail.com wrote:
> Ron N. wrote:
>
> > What you think is the first sample of the first movement, can't be
> > correctly bandlimited to the precision required unless the low pass
> > filter is fed the last sample of the last movement.
>
> There is no such thing as a bandlimited sample.  A sample is a scaled
> impulse, and an impulse is by definition for all frequencies.

Err... correct.  I should have said a sample of a sufficiently
bandlimited signal, where the pre-sampling low-pass filter
would presumably need support from at least the duration
of the entire symphony in order to produce it from a local
group of subsamples, in theory of course.

The thought experiment I was visualizing was using a very
wide FIR filter on an infinite width of sufficiently dense and
precise samples to do the proper bandlimiting.  ( It's been too
long since I've soldered any analog filter components :)


IMHO. YMMV.
-- 
rhn A.T nicholson d.O.t C-o-M

cs_posting@hotmail.com wrote:
> Ron N. wrote:
>
> > What you think is the first sample of the first movement, can't be
> > correctly bandlimited to the precision required unless the low pass
> > filter is fed the last sample of the last movement.
>
> There is no such thing as a bandlimited sample.  A sample is a scaled
> impulse, and an impulse is by definition for all frequencies.

Err... correct.  I should have said a sample of a sufficiently
bandlimited signal, where the pre-sampling low-pass filter
would presumably need support from at least the duration
of the entire symphony in order to produce it from a local
group of subsamples, in theory of course.

The thought experiment I was visualizing was using a very
wide FIR filter on an infinite width of sufficiently dense and
precise samples to do the proper bandlimiting.  ( It's been too
long since I've soldered any analog filter components :)


IMHO. YMMV.
-- 
rhn A.T nicholson d.O.t C-o-M

cs_posting@hotmail.com wrote:
> Ron N. wrote:
>
> > What you think is the first sample of the first movement, can't be
> > correctly bandlimited to the precision required unless the low pass
> > filter is fed the last sample of the last movement.
>
> There is no such thing as a bandlimited sample.  A sample is a scaled
> impulse, and an impulse is by definition for all frequencies.

Err... correct.  I should have said a sample of a sufficiently
bandlimited signal, where the pre-sampling low-pass filter
would presumably need support from at least the duration
of the entire symphony in order to produce it from a local
group of subsamples, in theory of course.

The thought experiment I was visualizing was using a very
wide FIR filter on an infinite width of sufficiently dense and
precise samples to do the proper bandlimiting.  ( It's been too
long since I've soldered any analog filter components :)


IMHO. YMMV.
-- 
rhn A.T nicholson d.O.t C-o-M

cs_posting@hotmail.com wrote:
> Ron N. wrote:
>
> > What you think is the first sample of the first movement, can't be
> > correctly bandlimited to the precision required unless the low pass
> > filter is fed the last sample of the last movement.
>
> There is no such thing as a bandlimited sample.  A sample is a scaled
> impulse, and an impulse is by definition for all frequencies.

Err... correct.  I should have said a sample of a sufficiently
bandlimited signal, where the pre-sampling low-pass filter
would presumably need support from at least the duration
of the entire symphony in order to produce it from a local
group of subsamples, in theory of course.

The thought experiment I was visualizing was using a very
wide FIR filter on an infinite width of sufficiently dense and
precise samples to do the proper bandlimiting.  ( It's been too
long since I've soldered any analog filter components :)


IMHO. YMMV.
-- 
rhn A.T nicholson d.O.t C-o-M