Repeat the previous problem for N = 13 N = 13 and k = 6 k = 6 . Use a Barker code of length

Repeat the previous problem for $N=13$ and $k=6$. Use a Barker code of length 13.

Data From Problem 13

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. 

Equation (6.31)

(b) Sketch the corresponding transversal filter output.

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