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

Explanation: An identical system is a system whose output is same as the input, that is it does not perform any operation on the input and transmits it.

Explanation: For example, the value of the output at the time n=0 is y(0)=x(1), that is the system is advanced by one unit.

Explanation: From the equation given, y(n)=x(n)+x(n-1)+x(n-2)+…. .This system calculates the running sum of all the past input values till the present time. So, it acts as an accumulator.

Explanation: If the function to this block is x(n) then the output from the block will be x(n-1). So, the block is called as delay block or delay element.

Explanation: An delay system is a system whose output is same as the input, but after a delay.

Explanation: Since the output of the system y(n) depends only on the present value of the input x(n) but not on the past or the future values of the input, the system is called as static or memory-less system.

Explanation: If the input is delayed by k units then the output will be y(n,k)=x(n-k)-x(n-k-1)
If the output is delayed by k units then y(n-k)=x(n-k)-x((n-k)-1)
=>y(n,k)=y(n-k). Hence the system is time-invariant.

Explanation: Given equation is y(n)=x²(n)
Let y₁(n)=x₁²(n) and y₂(n)=x₂²(n)
y₃(n)=y₁(n)+y₂(n)= x₁²(n)+ x₂²(n)≠(x₁(n)+x₂(n))²
So the system is non-linear.

Explanation: A system is said to be causal if the output of the system is defined as the function shown below
y(n)=F[x(n),x(n-1),x(n-2),…] So, according to the conditions given in the question, the system is a causal system.

Explanation: An arbitrary relaxed system is said to be BIBO stable if it has a bounded output for every value in the bounded input. So, the system given in the question is a Non-stable system.