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From: Steve Pope on 5 May 2010 08:56 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 5 May 2010 15:16 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 5 May 2010 15:24 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 5 May 2010 16:11 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 5 May 2010 22:06
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 |