Design a filter with 10 coefficients such that its impulse response approximates the following sequence: [g_{n}=left(frac{1}{6^{n}}+10^{-n}+frac{0.05}{n+2} ight)

Design a filter with 10 coefficients such that its impulse response approximates the following sequence:

\[g_{n}=\left(\frac{1}{6^{n}}+10^{-n}+\frac{0.05}{n+2}\right) u(n)\]

Choose a few key values for \(M\) and \(N\), and discuss which choice leads to the smallest mean-squared error after the tenth sample.