# Questions tagged [stochastic]

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### Stochastic approximation algorithm

The goal is to find the FIR filter coefficients $\mathbf{h} = [5;3]$ with the help of the adaptive FIR filter $\mathbf{w}$ of order $p = 2$. I have implemented the Stochastic approximation algorithm ...
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### Ergodicity of joint process

If we have two processes and both of them are ergodic. Does this mean that the joint proces is ergodic? Or other way around? If we have the dynamics for both components of the joint process what are ...
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### Variance Due to white noise input

I have the problem below. It sounds simple but for some reason I have been stuck on it for a long time and don't know what am doing wrong. Am trying to solve this using correlations. So we all know ...
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### When deriving the power spectral density of stochastic processes, why does taking an expectation allow the $T\rightarrow\infty$ limit to be taken?

I am following the arguments presented in the paper AN-255 Power Spectra Estimation, from Texas Instruments, to learn how to derive the power spectral density for a stationary stochastic process, and ...
80 views

### When a stochastic process would be a beneficial model in terms of noise

Let's say we have an image/signal with some noise in it. When would it be beneficial to model the signal as an outcome of a stochastic process? More specifically: How significant would noise have to ...
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### Test for Equivalence of two time series

I wish to test whether two time series are equal. So I believe best way to define equivalence is that given two time series, say $\{x1_t\}$ and $\{x2_t\}$, we show that both the series come from the ...
294 views

A basic theorem in communications is the matched filter maximizes the SNR at sampling. I'm a little confused on how this relates to discrete time systems and sampling rate. Normally if you sample at ...
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### Is ergodic in mean a property defined only for WSS stochastic processes?

I understand the definition of a random process $X(t)$ being ergodic in mean (first-order ergodic) is that the expectation of the sample mean \$<u_X>_T=\frac{1}{T} \int_{\frac{-T}{2}}^{\frac{T}{2}...