# Z - transform of white noise

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.

• 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 Commented Feb 26, 2021 at 15:57