Q$4)$ The two pulses $s_1(t)$ and $s_2(t)$ shown in Fig. Q$4$ are used to transmit binary data, such that $0"s_1(t)$ and $"1"s_2(t).($Note: $T$ is bit period$)$

a$)$ Determine and sketch the corresponding matched filters, $h_1(t)$ and $h_2(t).$

b$)$ Sketch the corresponding outputs of the two matched filters, $y_1(t)$ and $y_2(t)$ when the pulse $s_1(t)$ is applied at their input.