Consider an open loop system having a transfer function \(G(s)=(s+1)^{-1}\). Find its output \(c(t)\) in LPWM-GBPF domain for a step input \(u(t)\) using the convolution matrix. Consider \(m=8\) and \(T=1 \mathrm{~s}\), and choose the values of \(h_{0}\) and \(\delta\) to make MISE a minimum.

Compare the convolution results with direct expansion of the output and determine the percentage errors of different coefficients.