A binary baseband system transmits the pulse $$p(t)=\begin{cases}1/\sqrt{T_s},&0\le t\le T_s,\\0,&\text{otherwise}.\end{cases}$$ Which graphical choice shows its matched-filter output y(t)?
The matched filter impulse response is the time-reversed pulse $h(t)=p(T_s-t)$. Convolution of two equal rectangular pulses produces a triangle on 0≤t≤2Ts.
During the first interval its value is the overlap length t divided by Ts; after Ts it is (2Ts−t)/Ts. The peak at t=Ts equals the pulse energy, which is 1.
Thus the correct graph is **C**, with unit peak at Ts and zeros at 0 and 2Ts.
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