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Question

Consider a system S with input x[n] and output y[n] related by

y[n]=x[n]{g[n]+g[nāˆ’1]}

Select the correct statement about system S

A
If g[n] = 1 for all n, then S is time invariant.
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B
If g[n] = n for all n, then S is time variant.
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C
If g[n] = δ[n], then S is time variant.
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D
If g[n] = 1 + (-1)n, then S is time invariant.
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Solution

The correct option is D If g[n] = 1 + (-1)n, then S is time invariant.
(a) g[n] = 1

g[n - 1] = 1

So, y[n] = x[n] [1 + 1]

= 2 x[n]

Thus system is time invariant

(b) g[n] = n

So, g[n - 1] = (n - 1)

Now, y[n] = x[n] [n + n -1]

x[n] [2n - 1] which is time variant.

(c) g[n]=1+(1)n

g[n1]=1+(1)n1

y[n]=x[n][1+(1)n+1+(1)n1]

=x[n][2]

= 2x [n]

which is time invariant

(d) g[n] = δ[n]

g[n-1] = δ[n1]

g[n]=x[n][δ[n]+δ[n1]]


which is time variant.


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