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I am taking a graduate course in Digital signal processing with no prior knowledge in DSP. So I am struggling because I don't have the foundational knowledge. Please I need help with the following.

  1. Assume we have the following difference equation $y(n) = y(n-3) + w(n)$ where $w(n)$ is the white gaussian noise. The transfer function of the system is given by $ H(z) = \frac {Y(z)}{W(z)} =\frac{1}{1 – z^{-3}}$. The question is, how can we determine the $z$ transform of $W(z)$ assuming the white noise has zero mean and variance $\sigma^2 = x$.

  2. Should I perform my analysis in the frequency domain by transferring the transfer function from z domain to the frequency domain. I read that to do that we need to replace $z$ with $e^{j\omega} $ Any explanation will be greatly appreciated.

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    $\begingroup$ Hi @Tee, there is a dedicated forum on StackExchange just for digital signal processing, I suggest posting your question there if you have not done so already. I think the sampling would introduce a sinc function in the spectrum, but I don't feel confident answering this. Good luck $\endgroup$ – Pete W Feb 26 at 15:57

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