Q1. The relationship between the input x[n] and output y[n] of a certain discrete time system...
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Q1. The relationship between the input x[n] and output y[n] of a certain discrete time system is defined as below. Write an expression for each of the systems in terms of the convolution sum and find the impulse response h[n] of each of the systems. Sketch the block diagram of each system, and indicate with reason whether each system can be described as (1) LTI (ii) memoryless and (111) causal. (a) y[n] = 0.25x[n] +0.5x[n-1] +0.25x[n-2] (b) y[n] = 0.5x[n] +0.5x[n-2] (c)y[n]=0.5x[n]+0.5x[n-1] (d) Find the impulse response h[n] of the each of the systems above. Hint: write an expression for the convolution of y[n] = x[n] *h[n]. (e) Find the output y[n] of the each of the systems above when the input signal x[n] defined below is applied to the system. x[n] = [n, n=0,1,2,3,4 0, otherwise Q1. The relationship between the input x[n] and output y[n] of a certain discrete time system is defined as below. Write an expression for each of the systems in terms of the convolution sum and find the impulse response h[n] of each of the systems. Sketch the block diagram of each system, and indicate with reason whether each system can be described as (1) LTI (ii) memoryless and (111) causal. (a) y[n] = 0.25x[n] +0.5x[n-1] +0.25x[n-2] (b) y[n] = 0.5x[n] +0.5x[n-2] (c)y[n]=0.5x[n]+0.5x[n-1] (d) Find the impulse response h[n] of the each of the systems above. Hint: write an expression for the convolution of y[n] = x[n] *h[n]. (e) Find the output y[n] of the each of the systems above when the input signal x[n] defined below is applied to the system. x[n] = [n, n=0,1,2,3,4 0, otherwise
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43 Xn A Z 1 025 XZ 2 N H 05 025 It is LTI system ie linear Time invariant It depends on parts presen... View the full answer
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