Zero padding fftw

On Dec 14, 1:28&#4294967295;am, illywhacker <illywac...@gmail.com> wrote:
> On Dec 13, 9:02&#4294967295;pm, dbd <d...@ieee.org> wrote:
> ...

> > Yes it is imprecise, and intentionally so. In real world data
> > analysis, we expect that our samples contain components from unknown
> > models and even from models that cannot be accurately represented by a
> > finite set of samples.
...
>
> > we may use the anti-aliased and sampled (and therefore faulty) data to
> > determine if we have a signal with components that represent some
> > model even when we know that signals that fit the model cannot be
> > accurately represented by the anti-aliased sampled data sets.
...
>
> > To do
> > this for some models we may need to 'resolve' the positions of things
> > like peaks and zero crossings to a finer 'resolution' than allowed by
> > the original sample positions.
>
> It is very simple. Either the original sample positions uniquely
> encode the signal of interest or they do not. If they do, then
> computing further samples is trivial. If they do not (i.e. more than
> one signal of interest could have produced the given samples), then
> further information is needed to distinguish between these
> possibilities. This further information is a model. Which part of this
> do you not agree with?
>
> illywhacker;

Stochastic models aren't uniquely determined by a finite number of
samples. The samples we process from real world signals have been anti-
aliased and sampled by real world filters and samplers that add
stochastic components to the samples even if the signals do not
already contain them (which they do).

Your analysis only applies, as I've said, to symbolic manipulation and
homework problems (artificial data).

Dale B. Dalrymple

On Dec 14, 4:19 pm, dbd <d...@ieee.org> wrote:
> On Dec 14, 1:28 am, illywhacker <illywac...@gmail.com> wrote:
> > On Dec 13, 9:02 pm, dbd <d...@ieee.org> wrote:

> > It is very simple. Either the original sample positions uniquely
> > encode the signal of interest or they do not. If they do, then
> > computing further samples is trivial. If they do not (i.e. more than
> > one signal of interest could have produced the given samples), then
> > further information is needed to distinguish between these
> > possibilities. This further information is a model. Which part of this
> > do you not agree with?
>
> Stochastic models aren't uniquely determined by a finite number of
> samples. The samples we process from real world signals have been anti-
> aliased and sampled by real world filters and samplers that add
> stochastic components to the samples even if the signals do not
> already contain them (which they do).

Dale,

I did not say that the perfect reconstruction case was the real-world
case. I said *if*...*then*...

As you now say, at last agreeing with me, this is not the case in
practice. Therefore a model is needed that goes beyond this:

> 'The only "model" that is
> relevant to the situation is whether the signal of interest survived
> the anti-aliasing filtering required before the original sampling'

As to your little comments about homework: this is the typical
reaction of someone faced with the gaps in their knowledge and
seeking solace in the 'university of life' defence. The fact is that
all the DSP you are talking about, and probably all the DSP you know,
rather than being more sophisticated than any possible mathematical
approach because it deals with 'real-world' problems, is in fact
entirely equivalent to the *least* sophisticated developments of
mathematical DSP.

illywhacker;

On 12/14/2010 12:01 PM, illywhacker wrote:
> [...]

> The fact is that all the DSP you are talking about, and probably all
> the DSP you know, rather than being more sophisticated than any
> possible mathematical approach because it deals with 'real-world'
> problems, is in fact entirely equivalent to the *least*
> sophisticated developments of mathematical DSP.

Proof by assertion? If Dale's prescribed DSP is so simplistic, how
about some real meat, whoever you are?
-- 
Randy Yates                      % "My Shangri-la has gone away, fading like
Digital Signal Labs              %  the Beatles on 'Hey Jude'"
mailto://yates@ieee.org          %
http://www.digitalsignallabs.com % 'Shangri-La', *A New World Record*, ELO

On Dec 14, 2:13 am, Chris Bore <chris.b...@gmail.com> wrote:
>...

>
> Isn't one valid key point being made here, that if we have a set of
> samples that uniquely determine the signal, then no further
> information is added by any interpolation?

I don't think that anyone has actually suggested that interpolation
adds information. There have been people who have assumed that because
their personal (obviously the one true) definition of "resolution" is
a measure of information that the OP's use of "resolution" implies
added information. It doesn't.

Changes of basis don't need to add information to be useful. Just as
we resample in time to resolve features of interest like peaks and
zero crossings, we change bases via DFT to resolve the frequency
response without adding information.

...
> And isn't a second valid key point that in the case where the signal
> has been 'anti-aliased' to ensure that the first set of samples do
> uniquely determine it, then if we have additional knowledge of the
> signal prior to anti-aliasing (such as, that it is isolated point
> sources) then that a priori knowledge is added information and may be
> used to guide further analysis or processing.

Anti-aliasing doesn't convert the samples to uniquely determine the
signal, it converts the signal to another signal that might be
uniquely represented by the samples. Stochastic components aren't
uniquely determined by the samples. That's part of the a priori
knowledge that should guide further analysis and processing.

> ...

Dale B. Dalrymple

On Dec 14, 9:01&#4294967295;am, illywhacker <illywac...@gmail.com> wrote:
...
>
> As to your little comments about homework: this is the typical
> reaction of someone faced with the gaps in their knowledge and
> seeking solace in the 'university of life' defence. The fact is that
> all the DSP you are talking about, and probably all the DSP you know,
> rather than being more sophisticated than any possible mathematical
> approach because it deals with 'real-world' problems, is in fact
> entirely equivalent to the *least* sophisticated developments of
> mathematical DSP.
>
> illywhacker;

I'm sorry. I should have said "some homework problems". The limits on
stochastic components that I cite, and you say we agree on, are
inherent in the "mathematical DSP" of homework problems involving
signals in AWGN channels.

Dale B. Dalrymple

On Dec 14, 5:26&#4294967295;pm, dbd <d...@ieee.org> wrote:
> On Dec 14, 9:01&#4294967295;am, illywhacker <illywac...@gmail.com> wrote:
> ...
>
>
>
> > As to your little comments about homework: this is the typical
> > reaction of someone faced with the gaps in their knowledge and
> > seeking solace in the 'university of life' defence. The fact is that
> > all the DSP you are talking about, and probably all the DSP you know,
> > rather than being more sophisticated than any possible mathematical
> > approach because it deals with 'real-world' problems, is in fact
> > entirely equivalent to the *least* sophisticated developments of
> > mathematical DSP.
>
> > illywhacker;
>
> I'm sorry. I should have said "some homework problems". The limits on
> stochastic components that I cite, and you say we agree on, are
> inherent in the "mathematical DSP" of homework problems involving
> signals in AWGN channels.

I am not sure what you are trying to say. It sounds vaguely
conciliatory, but that may be a false hope. We agree that there is no
situation in which the signal of interests is uniquely known based on
the data. As soon as it is not uniquely known, further information,
i.e. a model, must be injected in order to make progress. This is a
very simple point, with which you decided to disagree several posts
ago. And yet someone of your intelligence surely cannot disagree with
this truism, so you must have misunderstood the point I was making.

illywhacker;

On Dec 14, 5:13&#4294967295;pm, Randy Yates <ya...@ieee.org> wrote:
> On 12/14/2010 12:01 PM, illywhacker wrote:
>
> > [...]
> > The fact is that all the DSP you are talking about, and probably all
> > the DSP you know, rather than being more sophisticated than any
> > possible mathematical approach because it deals with 'real-world'
> > problems, is in fact entirely equivalent to the *least*
> > sophisticated developments of mathematical DSP.
>
> Proof by assertion? If Dale's prescribed DSP is so simplistic, how
> about some real meat, whoever you are?

Randy,

Have you read all the previous posts, or are you just reacting to
something that irritates you?

illywhacker;

On Dec 14, 5:16&#4294967295;pm, dbd <d...@ieee.org> wrote:
> On Dec 14, 2:13 am, Chris Bore <chris.b...@gmail.com> wrote:

> > And isn't a second valid key point that in the case where the signal
> > has been 'anti-aliased' to ensure that the first set of samples do
> > uniquely determine it, then if we have additional knowledge of the
> > signal prior to anti-aliasing (such as, that it is isolated point
> > sources) then that a priori knowledge is added information and may be
> > used to guide further analysis or processing.
>
> Anti-aliasing doesn't convert the samples to uniquely determine the
> signal, it converts the signal to another signal that might be
> uniquely represented by the samples. Stochastic components aren't
> uniquely determined by the samples. That's part of the a priori
> knowledge that should guide further analysis and processing.

But a priori knowledge is a model! What are we disagreeing about?

illywhacker;

On 12/14/2010 04:57 PM, illywhacker wrote:
> On Dec 14, 5:13 pm, Randy Yates<ya...@ieee.org>  wrote:
>> On 12/14/2010 12:01 PM, illywhacker wrote:
>>
>>> [...]
>>> The fact is that all the DSP you are talking about, and probably all
>>> the DSP you know, rather than being more sophisticated than any
>>> possible mathematical approach because it deals with 'real-world'
>>> problems, is in fact entirely equivalent to the *least*
>>> sophisticated developments of mathematical DSP.
>>
>> Proof by assertion? If Dale's prescribed DSP is so simplistic, how
>> about some real meat, whoever you are?
>
> Randy,
>
> Have you read all the previous posts, or are you just reacting to
> something that irritates you?

I have read enough to know, like an old Ford, you blow a lot of smoke.
-- 
Randy Yates                      % "My Shangri-la has gone away, fading like
Digital Signal Labs              %  the Beatles on 'Hey Jude'"
yates@digitalsignallabs.com      %
http://www.digitalsignallabs.com % 'Shangri-La', *A New World Record*, ELO

On 12/14/2010 07:07 PM, Randy Yates wrote:
> On 12/14/2010 04:57 PM, illywhacker wrote:
>> On Dec 14, 5:13 pm, Randy Yates<ya...@ieee.org> wrote:
>>> On 12/14/2010 12:01 PM, illywhacker wrote:
>>>
>>>> [...]
>>>> The fact is that all the DSP you are talking about, and probably all
>>>> the DSP you know, rather than being more sophisticated than any
>>>> possible mathematical approach because it deals with 'real-world'
>>>> problems, is in fact entirely equivalent to the *least*
>>>> sophisticated developments of mathematical DSP.
>>>
>>> Proof by assertion? If Dale's prescribed DSP is so simplistic, how
>>> about some real meat, whoever you are?
>>
>> Randy,
>>
>> Have you read all the previous posts, or are you just reacting to
>> something that irritates you?
>
> I have read enough to know, like an old Ford, you blow a lot of smoke.

Joel.
-- 
Randy Yates                      % "My Shangri-la has gone away, fading like
Digital Signal Labs              %  the Beatles on 'Hey Jude'"
yates@digitalsignallabs.com      %
http://www.digitalsignallabs.com % 'Shangri-La', *A New World Record*, ELO