Ron N. wrote:> 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 :)No matter how you filter, a finite duration selection of the filter output still can't be bandlimited. The kind of band limiting we tend to worry about as engineers is the high frequency aliases... these are easy to deal with. But the leakage between some small fraction of a HZ, and true zero frequency, that we can't handle. And that is where the last movement of the symphony is hiding.
question about non-uniform sampling?
Started by ●November 12, 2005
Reply by ●November 16, 20052005-11-16
Reply by ●November 16, 20052005-11-16
Jerry Avins wrote:> 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.Nit pick -- that's not exactly what I said; there are conditions, in particular, the samples have to be at distinct positions among them and with respect to the other samples that are at uniform intervals.> 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/.I hope you're not still missing the part that you still have to wait an infinite amount of time before you can even begin to reconstruct. I don't see that your reasoning is leading to a contradiction, even when we use it in the practical case -- there would be a contradiction if the reasoning led to the conclusion that you can reconstruct a part of the signal before it has happened. But that's not what follows from my claim. You can only reconstruct signals that have already passed, so there's no contradiction there. Carlos --
Reply by ●November 16, 20052005-11-16
cs_posting@hotmail.com wrote:> Ron N. wrote: > > > 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 :) > > No matter how you filter, a finite duration selection of the filter > output still can't be bandlimited.True. But what I am hypothesizing is that a low pass filter on the order of a symphony duration in impulse response might not leak enough of that Hz which you mention below to allow pulling out the movement in "hiding". Then Jerry won't have a problem with non-causality, because a filter with this long an impulse response will have to hear the end of the symphony before sending the start (group delay) to the sampler.> The kind of band limiting we tend to worry about as engineers is the > high frequency aliases... these are easy to deal with. But the leakage > between some small fraction of a HZ, and true zero frequency, that we > can't handle. And that is where the last movement of the symphony is > hiding.IMHO. YMMV. -- ron A.T nicholson d.O.t C-o-M
Reply by ●November 16, 20052005-11-16
cs_posting@hotmail.com wrote:> Ron N. wrote: > > >>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 :) > > > No matter how you filter, a finite duration selection of the filter > output still can't be bandlimited. > > The kind of band limiting we tend to worry about as engineers is the > high frequency aliases... these are easy to deal with. But the leakage > between some small fraction of a HZ, and true zero frequency, that we > can't handle. And that is where the last movement of the symphony is > hiding.But which last movement? At least two composers have written completions for Schubert's 9th, the "Unfinished". Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●November 16, 20052005-11-16
cs_posting@hotmail.com wrote:> Ron N. wrote: > > >>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 :) > > > No matter how you filter, a finite duration selection of the filter > output still can't be bandlimited. > > The kind of band limiting we tend to worry about as engineers is the > high frequency aliases... these are easy to deal with. But the leakage > between some small fraction of a HZ, and true zero frequency, that we > can't handle. And that is where the last movement of the symphony is > hiding.But which last movement? At least two composers have written completions for Schubert's 9th, the "Unfinished". Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●November 16, 20052005-11-16
cs_posting@hotmail.com wrote:> Ron N. wrote: > > >>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 :) > > > No matter how you filter, a finite duration selection of the filter > output still can't be bandlimited. > > The kind of band limiting we tend to worry about as engineers is the > high frequency aliases... these are easy to deal with. But the leakage > between some small fraction of a HZ, and true zero frequency, that we > can't handle. And that is where the last movement of the symphony is > hiding.But which last movement? At least two composers have written completions for Schubert's 9th, the "Unfinished". Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●November 16, 20052005-11-16
cs_posting@hotmail.com wrote:> Ron N. wrote: > > >>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 :) > > > No matter how you filter, a finite duration selection of the filter > output still can't be bandlimited. > > The kind of band limiting we tend to worry about as engineers is the > high frequency aliases... these are easy to deal with. But the leakage > between some small fraction of a HZ, and true zero frequency, that we > can't handle. And that is where the last movement of the symphony is > hiding.But which last movement? At least two composers have written completions for Schubert's 9th, the "Unfinished". Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●November 16, 20052005-11-16
Ron N. wrote:> cs_posting@hotmail.com wrote: > >>Ron N. wrote: >> >> >>>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 :) >> >>No matter how you filter, a finite duration selection of the filter >>output still can't be bandlimited. > > > True. But what I am hypothesizing is that a low pass filter on > the order of a symphony duration in impulse response might > not leak enough of that Hz which you mention below to allow > pulling out the movement in "hiding". Then Jerry won't have > a problem with non-causality, because a filter with this long > an impulse response will have to hear the end of the symphony > before sending the start (group delay) to the sampler.If a symphony is played in a forest and there is no one to sample the last movement, how can the filter "hear" it? ... Jerry -- Engineering is the art of making what you want from things you can get. �����������������������������������������������������������������������
Reply by ●November 17, 20052005-11-17
Jerry Avins wrote:> If a symphony is played in a forest and there is no one to sample the > last movement, how can the filter "hear" it?If it's not input to the filter (with, say, 100 hours of group delay) then it's not output and can't be reconstructed. - rhn
Reply by ●November 17, 20052005-11-17
