Test: Discrete Time Systems in The Time Domain - Electrical Engineering (EE) MCQ

 ‘y’ will be periodic only if x attains the same value after some time, T. However, if x is a one-one discrete function, it may not be possible for some x[n].

The system would be unstable, as the output will grow out of bound at the maximally worst possible case.

For positive time, the output depends on the input at an earlier time, giving causality for this portion. However, at a negative time, the output depends on the input at a positive time, i.e. at a time in the future, rendering it non causal.

The output always depends on the input at a time in the future, rendering it anti-causal.

As we give two inputs, x1 and x2, and give an added input x1 and x2, we do not get the corresponding y1 and y2. Thus, additive rule is disturbed and hence the system is not linear.

A time shift in the input scale gives double the time shift in the output scale, and hence is time variant.

The function obeys both additivity and homogeneity properties. Hence, the function is linear.

The system is not linear, as x1² + x2² is not equal to (x1 + x2)².

A time shift of t0 will still result in an equivalent time shift of t0 in the output, and hence will be time invariant.

Recursive discrete-time system:

If a system output y(n) at time n depends on any number of past output values y(n – 1), y(n – 2), …, it is called a recursive system.

This system requires two multiplication, one addition, and one memory location. This is a recursive system which means the output at time n depends on any number of past output values.

So, a recursive system has the feedback output of the system into the input. This feedback loop contains a delay element.

Hence s(n - 2) depends on past value, it is an example of recursive system