The discrete time system described by y[n] = x(n2) is

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The discrete time system described by y[n] = x(n²) is—

1. Causal, linear and time-varying
2. Causal, non-linear and time varying
3. Non-causal, linear and time-invariant
4. Non-causal, non-linear and time-variant

Correct Option: C

The given discrete-time system is y[n] = x[n²]
● is linear since there is no constant term as well as square terms in input and output.
● non-causal since for any value of n except 0 and 1, output depends upon the future value of the input for example at n = – 1

y[– 1] = x[1²] = x[1]
y[2] = x[2²] = x[4]

i.e., output depends upon the future input.
● System is time-invariant since there is no time factor term i.e., n in the given equation.
Hence, alternative (C) is the correct choice.