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

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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.

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Related Book For  book-img-for-question

Digital Signal Processing System Analysis And Design

ISBN: 9780521887755

2nd Edition

Authors: Paulo S. R. Diniz, Eduardo A. B. Da Silva , Sergio L. Netto

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