Given the sequences [left.begin{array}{l}mathbf{x}=left[begin{array}{lll}1 & a & frac{a^{2}}{2}end{array} ight]^{mathrm{T}} mathbf{h}=left[begin{array}{lll}1 & -a & frac{a^{2}}{2}end{array} ight]^{mathrm{T}}end{array} ight}] represented in matrix notation: (a) Calculate the linear convolution

Given the sequences

\[\left.\begin{array}{l}\mathbf{x}=\left[\begin{array}{lll}1 & a & \frac{a^{2}}{2}\end{array}\right]^{\mathrm{T}} \\\mathbf{h}=\left[\begin{array}{lll}1 & -a & \frac{a^{2}}{2}\end{array}\right]^{\mathrm{T}}\end{array}\right\}\]

represented in matrix notation:

(a) Calculate the linear convolution between the sequences employing the \(z\) transform.

(b) For \(a=1\), compute the linear convolution using the overlap-and-add method when the second sequence is split into blocks of length 2, showing the partial results.