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(a) A Gaussian random variable with zero mean and variance $\sigma$ is input to a limiter with input output characteristic given by

$$\begin{array}{ll} e_{\text {out }}=e_{i n} & \text { for }\left|e_{\text {in }}\right|<\sigma \\ e_{\text {out }}=\sigma & \text { for } e_{i n} \geq \sigma \\ e_{\text {out }}=-\sigma & \text { for } e_{\text {ln }} \leq \sigma \end{array}$$

Determine the probability density function of the output random variable.

(b) A random process $X(t)$ is wide sense stationary. If

$$Y(t)=x(t)-x(t-a)$$

Determine the auto correlation function $R_y(i)$ and power spectral density $S_y(\omega)$ of $Y(t)$ in terms of those of $X(t)$.