Convolution is a mathematical operation that expresses a relationship between an input signal, the output signal, and the impulse response of a linear-time invariant system. Three systems that represented by the impulse response, h[n], h2[n] and hz[n] are connected in series as shown in Figure Q2(a), where x[n] and y[n] are the input and output signals respectively. The impulse response functions of each system are represented by equation (1), (2) and (3). h[n] = nu[n + 4] – nu[n – 2] (1) h2[n] = d[n – 2] (2) hz[n] = 6[n + 3] – 28[n – 1] (3) | x[n] h, [n] h2[n] hz[n] →y[n] Figure Q2(a) (а) Using the convolution, sketch the output response of y[n] if the input signal is given by x[n] = 8[n].

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