Derive the block pulse function (BPF) coefficients for the functions given in Problem 2.3.

Data From Problem 2.3

Derive the Walsh coefficients for the following functions for \(m=4\) :
a. \(f(t)=\left\{\begin{array}{l}0,0 \leq t<\frac{1}{4} s \\ 1, \frac{1}{4} \leq t<\frac{2}{4} s \\ 0, \frac{2}{4} \leq t<\frac{4}{4} s\end{array}ight.\)
b. \(f(t)=\sin t, 0 \leq t<1 \mathrm{~s}\)
c. \(f(t)=\mathrm{K} t, 0 \leq t<1 \mathrm{~s}\), where \(\mathrm{K}\) is a positive constant.