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 Apr 26 awarded Teacher 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. Oct 9 comment convergence of autocorrelation function and existence of Fourier transform And also wondering how I can make sure if the autocorrelation function is absolutely integrable... Thank you in advance.