Is the system $y(n)=x(n^2)$ time invariant?

1. Is y/n )= x N 2 time invariant?
2. How do you know if a system is time invariant?
3. Is Y n )= x (- n time invariant?
4. Is the system Y N x N 2 )] 2 linear?

Is y/n )= x N 2 time invariant?

Hence, the given system is linear. For a system to be time invariant time delay of the input signal leads to an identical time shifts in the input signal. Similarly, when output changes by same amount n₀. Therefore, this system is time invariant.

How do you know if a system is time invariant?

A system is time-invariant if its output signal does not depend on the absolute time. In other words, if for some input signal x(t) the output signal is y1(t)=Trx(t), then a time-shift of the input signal creates a time-shift on the output signal, i.e. y2(t)=Trx(t−t0)=y1(t−t0).

Is Y n )= x (- n time invariant?

A system that reverses the signal cannot be time-invariant because when you shift the input, the output is shifted the other way. k and −k are not the same amount.

Is the system Y N x N 2 )] 2 linear?

Is the function y[2n] = x[2n] linear in nature? Explanation: The function obeys both additivity and homogeneity properties. Hence, the function is linear.