Expand the function \(f(t)=1-\exp (-t)\) in BPF domain with \(m=8\) and \(T=1 \mathrm{~s}\) and plot the result along with the exact curve of \(f(t)\).

Also, obtain the approximation of the scaled function \(f(t / \lambda)\) using the stretch matrix \(\mathbf{S}_{\mathrm{B}}\) in BPF domain, where \(\lambda=0.5\). Draw the BPF expanded forms of \(f(t)\) and \(f(t / \lambda)\) in a same plot.