Assume t = 0.5 s t = 0.5 s . (a) Give an expression for the autocorrelation of the signal s

Assume $\Delta t=0.5\mu s$. 

(a) Give an expression for the autocorrelation of the signal $s\left(t\right)$ and for the output of the matched filter when the input is $s(t-10\Delta t)$. 

(b) Compute the time bandwidth product, the increase in the peak SNR, and the compression ratio. (a) Perform the discrete convolution between the sequence $R_{11}$ defined in Eq. (6.31) and the transversal filter impulse response. (b) Sketch the corresponding transversal filter output.

Equation (6.31)

Hs(t)=x(t)+n(t).