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seen Jun 23 at 4:18

Apr
26
awarded  Teacher
Mar
12
asked approximation by superpositions of a sigmoidal function
Dec
10
comment convergence of autocorrelation function and existence of Fourier transform
Thank for your answer, Sanchez. But if the estimate of power spectral density had infinity, is the estimate still correct? Isn't it inconsistent? I am also wondering the existence..
Dec
10
accepted convergence of autocorrelation function and existence of Fourier transform
Nov
28
revised Can I say that if a kernel is translation-invariant (or shift-invariant), then the kernel is symmetric?
edited tags
Nov
28
revised Can I say that if a kernel is translation-invariant (or shift-invariant), then the kernel is symmetric?
edited tags
Nov
28
comment Can I say that if a kernel is translation-invariant (or shift-invariant), then the kernel is symmetric?
I edited my question. I was trying to understand the relation between translation invariance and symmetry...
Nov
28
revised Can I say that if a kernel is translation-invariant (or shift-invariant), then the kernel is symmetric?
added 209 characters in body; edited title
Nov
27
asked Can I say that if a kernel is translation-invariant (or shift-invariant), then the kernel is symmetric?
Nov
5
asked ROC analysis: detection probability when false alarm is maximized.
Oct
18
awarded  Commentator
Oct
18
comment some facts about $L_p$ space
Thank you guys for your answers.
Oct
17
awarded  Tumbleweed
Oct
16
asked some facts about $L_p$ space
Oct
11
comment convergence of autocorrelation function and existence of Fourier transform
Thank you very much, Chaohuang. Can I ask one more question for sure? In the literature, the wiener-khinchin theorem assumes the autocorrelation function is absolutely integrable because of the existence of Fourier transform. Although the autocorrelation function is not necessarily absolutely integrable, we can use the Wiener-Khinchin theorem after assuming it is integrable. Am I right?
Oct
10
comment convergence of autocorrelation function and existence of Fourier transform
It is rectangular in frequency domain. But the sinc function is square integrable which is weak condition for the existence of Fourier transform. Do you have any other examples for not necessarily absolute-integrable but the existence of Fourier transform? Many thanks.
Oct
10
comment convergence of autocorrelation function and existence of Fourier transform
If the autocorrelation function is not integrable, how can I use "Lebesgue-dominated-convergence theorem" that is considered in the proof of Wiener-Khinchin theorem?
Oct
10
answered convergence of autocorrelation function and existence of Fourier transform
Oct
10
comment convergence of autocorrelation function and existence of Fourier transform
Still, I am wondering how you make sure the correlation "strength" between two points decay faster. Is it always this? $r(0) \ge r(1) \ge r(2) \ge r(3) ...$
Oct
10
comment convergence of autocorrelation function and existence of Fourier transform
Ok. I think I have to understand the difference between signal power (or energy) and power (or energy) spectral density first. I thought average power of signal with finite energy is zero as $T$ goes to $\infty$. If non-zero power, energy is infinite. Let me explain these equations below.