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(Solved): An LTI system is described by the difference equation y[n]=x...

An LTI system is described by the difference equation

y[n]=x[n]-2x[n-1] x[n-2]

. Its output signal

y[n]

approximates computation of the second derivative of the input signal

x[n]

. i) Calculate and sketch the system impulse response

h[n]

(recall that

h[n]=y[n]

when

x[n]=\delta [n]

). Is this a causal system? Is it (BIBO) stable? State reasons for your answers. ii) Consider the input signal

x[n]=[1,4,9]

(in this vector representation of

x[n]

, the underlined sample is the sample at time index

n=0

; sample values at other time indices not listed have zero values). Calculate the output

y[n]=x[n]^(**)h[n]

over

-1<=n<=6

, where ***denotes linear convolution. Use a tabular approach to evaluate the convolution. Over what time indices

n

is the output

y[n]

neither transient nor end effect? Briefly explain, iii) Compute

y[n]=h[n]^(**)x[n]

numerically using the Matlab function 'conv' and check your answer to part (ii) above. Is the length of

y[n]

as expected? Explain. [Hint: type "help conv" in the Matlab command window to learn more about the input and output arguments of the "conv" function].

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