The output of a filter is given by 𝑦(𝑛) = cos(𝛼) ∙ 𝑥(𝑛) + sin(𝛼) ∙ 𝑥(𝑛 − 1) e) In real applications, you have mostly acc

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The output of a filter is given by 𝑦(𝑛) = cos(𝛼) ∙ 𝑥(𝑛) + sin(𝛼)∙ 𝑥(𝑛 − 1)
e) In real applications, you have mostly access to independent,zero mean, unit-variance Gaussian distributed samples 𝑤(𝑛). How canyou built (from 𝑤(𝑛)) samples 𝑥(𝑛) with power spectral density asin point b)? Verify on Matlab.
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b) The random input signal 𝑥(𝑛) consists of zero mean Gaussiandistributed samples with power spectral density 𝑅𝑋𝑋,𝛽(𝑓) = rect ((𝑓− 𝛽/2)/𝛽) , 𝑓 ∈ 0,1 , 𝛽 𝜖 [0,1]. Find the powerspectral density 𝑅𝑌𝑌,𝛼,𝛽(𝑓) of output 𝑦(𝑛).