A SISO DT LTI system having input x[n] and output is described by the difference equation...

A SISO DT LTI system having input x[n] and output is described by the difference equation y[n] = 0.5x[n] + 0.5x[n-1]. Obtain the unit sample response of the system by solving the difference equation. ( DO NOT USE LaPlace transforms or Z transforms)

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Expert Solution

Assuming the LTI system is causal, which is practical to implement.

given

Replace y by h and x by delta function, to find the unit sample response

now, put n = 0,1 2,3, and so on and solve for h[n] for all n till consecutive values get a value of 0.

put n=0

but delta function is defined(=1) only for n = 0, and =0 for all other n values,

put n=1

put n=2

From here onwards all values become 0, because of delta fuction exits only for n = 0.

Manojponduru answered 1 year ago

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