From: Steve Pope on
Alfred Bovin <alfred(a)bovin.invalid> wrote:

>"Steve Pope" <spope33(a)speedymail.org> wrote in message

>> (The question I find more interesting is what does it mean
>> when the PSD evaluates to a negative value at a positive
>> frequency....but this is unrelated.)

>How can it do that?

For some signals and some windows functions it can sometimes
happen. Beyond that, I am not certain what conditions lead
to this. It is usually rare, and the negative values can
usually be ignored.

Steve
From: Randy Yates on
On May 5, 8:56 am, spop...(a)speedymail.org (Steve Pope) wrote:
> Alfred Bovin <alf...(a)bovin.invalid> wrote:
> >"Steve Pope" <spop...(a)speedymail.org> wrote in message
> >> (The question I find more interesting is what does it mean
> >> when the PSD evaluates to a negative value at a positive
> >> frequency....but this is unrelated.)
> >How can it do that?
>
> For some signals and some windows functions it can sometimes
> happen.  Beyond that, I am not certain what conditions lead
> to this.   It is usually rare, and the negative values can
> usually be ignored.
>
> Steve

Steve, were you having a senior moment? :) X(f)*X*(f) is always non-
negative.

--Randy
From: Gordon Sande on
On 2010-05-05 16:16:33 -0300, Randy Yates <yates(a)ieee.org> said:

> On May 5, 8:56�am, spop...(a)speedymail.org (Steve Pope) wrote:
>> Alfred Bovin <alf...(a)bovin.invalid> wrote:
>>> "Steve Pope" <spop...(a)speedymail.org> wrote in message
>>>> (The question I find more interesting is what does it mean
>>>> when the PSD evaluates to a negative value at a positive
>>>> frequency....but this is unrelated.)
>>> How can it do that?
>>
>> For some signals and some windows functions it can sometimes
>> happen. �Beyond that, I am not certain what conditions lead
>> to this. � It is usually rare, and the negative values can
>> usually be ignored.
>>
>> Steve
>
> Steve, were you having a senior moment? :) X(f)*X*(f) is always non-
> negative.
>
> --Randy

If the window concerned was being applied in the lag domain it is quite
possible. In fact positive definite lag windows are not that common
compared to lag windows which have lower variance and are unbiased but have
the technical bother of permitting negative estimates of a parameter which is
known to be positive.


From: Steve Pope on
Randy Yates <yates(a)ieee.org> wrote:

>On May 5, 8:56�am, spop...(a)speedymail.org (Steve Pope) wrote:

>> For some signals and some windows functions it can sometimes
>> happen. �Beyond that, I am not certain what conditions lead
>> to this. � It is usually rare, and the negative values can
>> usually be ignored.

>Steve, were you having a senior moment? :) X(f)*X*(f) is always non-
>negative.

Well you have to drill down a bit more.

X(t) -> window -> sum(X(t)-(X(t-u)) -> window -> cosine transform ->
some non-positive-values. Depending on signal and window.

Odd stuff it is.


Steve
From: dbd on
On May 5, 1:11 pm, spop...(a)speedymail.org (Steve Pope) wrote:
> Randy Yates  <ya...(a)ieee.org> wrote:
>
> >On May 5, 8:56 am, spop...(a)speedymail.org (Steve Pope) wrote:
> >> For some signals and some windows functions it can sometimes
> >> happen.  Beyond that, I am not certain what conditions lead
> >> to this.   It is usually rare, and the negative values can
> >> usually be ignored.
> >Steve, were you having a senior moment? :) X(f)*X*(f) is always non-
> >negative.
>
> Well you have to drill down a bit more.
>
> X(t) -> window -> sum(X(t)-(X(t-u)) -> window -> cosine transform ->
> some non-positive-values.  Depending on signal and window.
>
> Odd stuff it is.
>
> Steve

Let's see now...
Someone takes a signal, windows, samples, applies a known high
variance estimator [1 sections 2,3] in a processing chain, discovers
that this does not produce results equivalent to the (infinite/
continuous) theoretical model, becomes surprised, reports results and
surprise and has the report met with disbelief.
What is unusual about this? On comp.dsp, nothing.

Dale B. Dalrymple

[1] Marple, S.L., Jr., “A tutorial overview of modern spectral
estimation”,
Acoustics, Speech, and Signal Processing, volume 4, 23-26,
Page(s):2152 - 2157, May 1989
available at:
http://www.cactus.org/~benjamin/X/marple.pdf