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(Solved): 3(a) Calculate the convolution of the two signals y[n] = x[n] *h[n], where x[n] is defined in Fig. 1 ...



3(a) Calculate the convolution of the two signals y[n] = x[n] *h[n], where x[n] is defined in Fig. 10 and h[n] is defined in Eqn 15. 

3(b) In fig 10, move the convolution machine from left to right and calculate y[n] by hand for n=0 to 4. 

Fig 10. 
Figure 10. Convolution machine with exponential function
Eqn 15: 
\( h[n]=\left(\frac{1}{2}\right)^{n} u[n]=\sum_{i=0}^{\infty}\left(\frac{1}{2}\right)^{i} \delta[n-i] \)
Figure 10. Convolution machine with exponential function \( h[n]=\left(\frac{1}{2}\right)^{n} u[n]=\sum_{i=0}^{\infty}\left(\frac{1}{2}\right)^{i} \delta[n-i] \)


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We will use definition of convolution sum and the defining property of u[n].
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