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Marcus Müller
Marcus Müller
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Assume that we have $y_k = s_k + n_k $. 

We have observed $y_k$ and want to estimate $s_k$. The goal is to use LMMSE (Linear MMSE) estimator to find $y_k$ and on the other hand, we know that our filter is causal, it means we have $\hat{s_k} = \sum_{m=-\infty}^k = h_{k-m}y_m$,

$$\hat{s_k} = \sum\limits_{m=-\infty}^k h_{k-m}y_m\text,$$ but why should $s_k$ and $y_k$ be jointly WSS?

Assume that we have $y_k = s_k + n_k $. We have observed $y_k$ and want to estimate $s_k$. The goal is to use LMMSE (Linear MMSE) estimator to find $y_k$ and on the other hand, we know that our filter is causal, it means we have $\hat{s_k} = \sum_{m=-\infty}^k = h_{k-m}y_m$, but why should $s_k$ and $y_k$ be jointly WSS?

Assume that we have $y_k = s_k + n_k $. 

We have observed $y_k$ and want to estimate $s_k$. The goal is to use LMMSE (Linear MMSE) estimator to find $y_k$ and on the other hand, we know that our filter is causal, it means we have

$$\hat{s_k} = \sum\limits_{m=-\infty}^k h_{k-m}y_m\text,$$ but why should $s_k$ and $y_k$ be jointly WSS?

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user137927
user137927
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Why is being jointly WSS important in signal estimation with LMMSE estimator?

Assume that we have $y_k = s_k + n_k $. We have observed $y_k$ and want to estimate $s_k$. The goal is to use LMMSE (Linear MMSE) estimator to find $y_k$ and on the other hand, we know that our filter is causal, it means we have $\hat{s_k} = \sum_{m=-\infty}^k = h_{k-m}y_m$, but why should $s_k$ and $y_k$ be jointly WSS?