2.1 Consider a discrete-time non-periodic signal x[k] and the period signal y[k] shown in Fig. Q2.1(a)...

   

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2.1 Consider a discrete-time non-periodic signal x[k] and the period signal y[k] shown in Fig. Q2.1(a) and Fig. Q2.1(b) respectively. 5 2.3 4 3 2 1 x[k] Fig. Q2.1(a) 2.1.2 Determine the energy size of x[k]. 1 2 4 If x[k] = 5 cos 2.1.2 Determine the power size of y[k]. Злк y[k] ::TTTTTT. 0 K Fig. Q2.1(b) 2 4 € is periodic, find the fundamental period No. 2.4 A filter is described by y[k]=x[k+1]-x[k]+x[k-1]. 2.4.1 Determine the impulse response of the filter h[k]. 2.4.2 Find the zero-state response y[k] if the input is x[k] = k² (u[k]-u[k-4]). Plot y[k]. Hint: Use the property of convolution of a function with an impulse. (12) 2.1 Consider a discrete-time non-periodic signal x[k] and the period signal y[k] shown in Fig. Q2.1(a) and Fig. Q2.1(b) respectively. 5 2.3 4 3 2 1 x[k] Fig. Q2.1(a) 2.1.2 Determine the energy size of x[k]. 1 2 4 If x[k] = 5 cos 2.1.2 Determine the power size of y[k]. Злк y[k] ::TTTTTT. 0 K Fig. Q2.1(b) 2 4 € is periodic, find the fundamental period No. 2.4 A filter is described by y[k]=x[k+1]-x[k]+x[k-1]. 2.4.1 Determine the impulse response of the filter h[k]. 2.4.2 Find the zero-state response y[k] if the input is x[k] = k² (u[k]-u[k-4]). Plot y[k]. Hint: Use the property of convolution of a function with an impulse. (12)