$4$

Consider an eight$-$tone OFDM system transmitting a time domain baseband signal $u[n]=\{1,4,3,2,1,3,1,2\}$ over a channel with an impulse response of $h[n]=\{2,0,2,-1\}.$

$-$What is the minimum required length of the cyclic prefix?

Plot the signal vector for:

$u[n]$

$\frac{?}{\text{b}\text{a}\text{r}}(u)[n]=u[n]$ with cyclic prefix

$\frac{?}{\text{b}\text{a}\text{r}}(y)[n]=$ after passing through the channel $h[n]$

$y[n]=$ after cyclic prefix deletion

$Y[k]=$ FFT output of $y[n]$

hat$(S)[k]=Y\frac{k}{H}[k]$

hat$(s)[n]=$IFFT of hat$(S)[k]$