## Digital Signal Processing Questions and Answers Part-5

1. The output signal when a signal x(n)=(0,1,2,3) is processed through an ‘Identical’ system is?
a) (3,2,1,0)
b) (1,2,3,0)
c) (0,1,2,3)
d) None of the mentioned

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.

2. If a signal x(n) is passed through a system to get an output signal of y(n)=x(n+1), then the signal is said to be ____________
a) Delayed
c) No operation
d) None of the mentioned

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.

3. If the output of the system is $$y(n)=\sum_{k=-\infty}^nx(y)$$ with an input of x(n) then the system will work as ___________
a) Accumulator
c) Subtractor
d) Multiplier

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.

4. What is the output y(n) when a signal x(n)=n*u(n)is passed through a accumulator system under the conditions that it is initially relaxed?
a) $$\frac{n^2+n+1}{2}$$
b) $$\frac{n(n+1)}{2}$$
c) $$\frac{n^2+n+2}{2}$$
d) None of the mentioned

Explanation: Given that the system is initially relaxed, that is y(-1)=0
According to the equation of the accumulator,
y(n)=$$∑_{k=-∞}^n x(n)$$
=$$∑_{k=-∞}^{-1} x(n)+∑_{k=0}^n x(n)$$
=$$y(-1)+ ∑_{k=0}^n n*u(n)$$
=$$0+∑_{k=0}^n n$$(since u(n)=1 in 0 to n)
=$$\frac{n(n+1)}{2}$$

5. The output signal when a signal x(n)=(0,1,2,3) is processed through an ‘Delay’ system is?
a) (3,2,1,0)
b) (1,2,3,0)
c) (0,1,2,3)
d) None of the mentioned

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

6. The system described by the input-output equation y(n)=nx(n)+bx3(n) is a __________
a) Static system
b) Dynamic system
c) Identical system
d) None of the mentioned

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.

7. Whether the system described by the input-output equations y(n)=x(n)-x(n-1) a Time-variant system.
a) True
b) False

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.

8. The system described by the input-output equations y(n)=x2(n) is a Non-linear system.
a) True
b) False

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.

9. If the output of the system of the system at any ‘n’ depends only the present or the past values of the inputs then the system is said to be __________
a) Linear
b) Non-Linear
c) Causal
d) Non-causal