$2.$ Consider an NRZ$-$I $($mid$-$bit transition$)$ rectangular pulsed baseband

transmission system, which is transmitting the following bits:

$100110111011($Assume that the MSB is the first transmitted bit$).$ The

data rate is R and the voltage levels are $$V

a$.(5$ points$)$ Sketch the transmitted waveform. Assume the signal

before the first transmitted bit is at $$V$.$ Let$$s call this waveform

x$($t$).$ Show all bit times and transition times.

b$.(5$ points$)$ Calculate the observed baud rate for this transmission

c$.$ Let$$s design a receiver system for this transmission assuming a

noise$-$less reception. The block diagram for this receiver is

shown below in Figure $1$

Figure $1$: NRZ$-$I receiver system

i$.(2$ points$)$ Mathematically describe the operation $$A$$ in

the time domain

ii$.(3$ points$)$ Sketch y$($t$).$ Show all time intercepts and

amplitude values.

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iii. $(2$ points$)$ Give a general mathematical expression for Ts

$($sampling interval$)$

iv$.(3$ points$)$ Mathematically describe the detection rule $$B$$