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You need the joint distribution of $X_{t_1}$ and $X_{t_2}$ in order to calculate $E[X_{t_1}X_{t_2}]$ and nobody has claimed that the joint distribution of $X_{t_1}$ and $X_{t_2}$ is the same as the joint distribution of $X_{t_1}$ and $X_{t_3}$. Stationarity requires that the joint distribution of $X_{t_1}$ and $X_{t_2}$ be the same as the joint distribution ...

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I have churn over this question for a very long time. I never liked how answers to this question are again presented in mathematical form. Nevertheless, i continued looking at the same problem over and over again and whatever i have understood is represented below. In this way i understood why frequency axis of PSD still represents the frequency of a time-...

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I believe that h(-t) means a "time-reversed" version of h(t). Your command: 'y = conv(r,-h);' computes the convolution of 'r' and negative 'h', and you don't want that. I think you want: y = conv(r,conj(fliplr(h)));

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