Let x be a finite sequence with DFT

$ X=\operatorname{DFT}[x]=[0,1+j, 1,1-j] $

Using the properties of the DFT determine the DFT's of the following:

i) $y[n]=e^{j(\pi / 2) n} x(n)$

ii) $y[n]=\cos (\pi / 2) n \ x(n)$

iii) $y[n]=x[(n-1)_4]$

iv $y[n]=[0,0,1,0] \oplus x[n]$ with $\oplus$ denoting circular convolution

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