Solution:

We have,

$ y(n)=\frac{1}{N} \sum_{k=0}^{N-1} Y(k) e^{\frac{j 2 \pi n n}{N}}, \quad n=0,1 \ldots . . N-1\\ $

For $\mathrm{N}=4$

$ y(n)=\frac{1}{4} \sum_{k=0}^3 Y(k) e^{\frac{j 2 \pi k n}{4}}, \quad n=0,1,2,3\\ $

For $\mathrm{n}=0$

$ \begin{aligned} y(0) & =\frac{1}{4} \sum_{k=0}^3 Y(k) \\\\ & =\frac{1}{4}[y(0)+y(1)+y(2)+y(3)] \\\\ & =\frac{1}{4}[1+0+1+0] \\\\ & …