1. Which of the following system is causal?
a) y[n] = 2[n] – 3[n+1]
b) y[n] = 2[n] + 3
c) y[n] = 2[n-7] – 3[n+1]
d) y[n] = 2[n]*3[n+1]
Explanation: An LTI system is said to be causal only when its output at any time depends on the previous or present value of the input. A causal system cannot depend on the future values of the input.
2. When are LTI systems stable?
a) Only when bounded input produces a bounded output
b) Only when bounded input produces a unbounded output
c) Only when unbounded input produces a bounded output
d) Only when unbounded input produces an unbounded output
Explanation:It follows from previous BIBO stability factor. It is the same for an LTI system too. Hence, a continuous or discrete time LTI system is said to be stable only when bounded input produces a bounded output.
3. Is discrete time convolution possible?
a) True
b) False
Explanation: Yes, like continuous time convolution discrete time convolution is also possible with the same phenomena except that it is discrete and superimposition occurs only in those time interval in which signal is present.
4. How is discrete time convolution represented?
a) x[n] + h[n]
b) x[n] – h[n]
c) x[n] * h[n]
d) x[n] + h[n]
Explanation: Discrete time convolution is represented by x[n]*h[n]. Here x[n] is the input and h[n] is the impulse response
5. What are the tools used in a graphical method of finding convolution of discrete time signals?
a) Plotting, shifting, folding, multiplication, and addition in order
b) Scaling, shifting, multiplication, and addition in order
c) Scaling, multiplication and addition in order
d) Scaling, plotting, shifting, multiplication and addition in order
Explanation: The tools used in a graphical method of finding convolution of discrete time signals are basically plotting, shifting, folding, multiplication and addition. These are taken in the order in the graphs. Both the signals are plotted, one of them is shifted, folded and both are again multiplied and added.
6. Choose the correct equation for finding the output of a discrete time convolution?
a) y[n] = ∑x[k]h[n-k], k from 0 to ∞
b) y[n] = ∑x[k]h[n-k], k from -∞ to +∞
c) y[n] = ∑x[k]h[k], k from 0 to ∞
d) y[n] = ∑x[k]h[n], k from -∞ to +∞
Explanation: y[n]=∑x[k]h[n-k], k from -∞ to +∞
Is the correct equation, where x[n] is the input and h[n] is the impulse response of the ∂[n] input of an LTI system. This is referred to as the convolution sum.
7. What is a convolution sum?
a) ∑x[k]h[n-k], k from -∞ to +∞
b) ∑x[k]*∑h[n-k], k from -∞ to +∞
c) ∑x[k]+∑h[n-k], k from -∞ to +∞
d) ∑∑x[k]h[n-k], k from -∞ to +∞
Explanation: y[n]=∑x[k]h[n-k], k from -∞ to +∞, y[n] is the output of the summation of the components on the right hand side. Where x[n] is the input of an LTI system and h[n] is the impulse response of the ∂[n] input of an LTI system. The response is due to superposition, in short.
8. What is the convolution of x[n]=e-n2 and h[n]=n2?
a) 5.318n2 + .123
b) 6.318n2 + .123
c) 5.318n+.88
d) 5.318n2+.8846
Explanation: x[n]*h[n]=∑x[k]h[n-k] =∑e-k2[(n-k)2] =3n2∑e-k2 + ∑k2 e-k2
=5.318n2+.8846.
9. Choose the properties which are followed by a discrete time convolution?
a) Associative, commutative, distributive
b) Associative
c) Commutative and distributive
d) Distributive and associative
Explanation: The properties which are followed by a discrete time convolution are same as continuous time convolution. These are – associative, commutative, distributive property.
10. What is the convolution of a signal with an impulse?
a) Signal itself
b) Impulse
c) A new signal
d) Signal multiplied by impulse
Explanation: The convolution of a signal x(n) with a unit impulse function ∂(n) results in the signal x(n) itself:
x(n)* ∂(n)=x(n).