Consider the system of Problem 10.1. For the same values of \(m\) and \(T\), find its output \(c(t)\) in conventional BPF domain using the convolution matrix. Finally, compare the convolution result with the result obtained above in LPWM-GBPF domain with respect to MISE.

Data From Problem 10.1

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.