This set of Signals & Systems MCQs focuses on “The Impulse Function – 2”.
1. What is the other name of a Continuous Time Unit Impulse Function?
a) Dirac delta function
b) Unit function
c) Area function
d ) Direct delta function
Explanation: The continuous time unit impulse function is also known as the Dirac delta function. This because it was first defined by Paul Adrein Maurice Dirac as ∂(t)=0.
2. What is the area of a Unit Impulse function?
b) Half of Unity
c) Depends on the function
Explanation: The area under an impulse function is unity. It is defined between limits negative infinity to positive infinity with ∂(t)dt=1, i.e ∫∂(t)dt=1. It can be seen as a rectangular pulse with width that is negligible and the height that is infinitely large and area as one.
3. Why is the impulse duration important?
a) It is zero
b) It changes with time
c) It approaches zero
d) It depends on the situation
Explanation: One of the most interesting features of the impulse function, is not its shape, but the fact that its effective duration (pulse width) approaches zero, while the area remains unity. Hence, ∫∂(t)dt=1.
4. What are the singularity functions?
a) Derivatives and integrals of unit impulse functions
b) Derivatives of a unit impulse function
c) Integrals of an impulse function
d) Sum of successive impulse function
Explanation: All the function derived from an impulse function(successive derivatives and integrals) are called singularity functions. Here, impulse function is taken as a generalized function than an ordinary function.
5. What properties does a Continuous time unit Impulse function follow?
a) Shifting, sampling, differentiation, multiplication
b) Multiplication, sampling, shifting
c) Shifting, multiplication, differentiation
d) Sampling only
Explanation: Continuous time impulse functions follows all the properties like shifting, scaling, sampling or multiplication property, differential.
6. Impulse function is an odd function.
Explanation: The Impulse Function is an even function. By scaling property of an Impulse function we can see, ∂(at)=1/|a|∂(t)
So, substituting, ∂(-t)=1/|-1|∂(t) we get ∂(t), hence, it is an even function. (∂ = del operator).
7. Multiplication of a signal with a Unit Impulse function gives the value of the signal at which the impulse is located.
Explanation: Multiplying the signal by a unit impulse samples the value of the signal at the point at which the impulse is located. That is x(t)*∂(t)=x(t)|t=0=x(0)∂(t).
8. What is a doublet function?
a) Branch of an impulse function
b) The output of an impulse function
c) The first derivative of an impulse function
d) Any continuous time impulse function has another name that is doublet function
Explanation: The first derivative of d∂(t)/∂(t)=∂’(t) is referred to as a doublet function. The derivatives of all orders of the impulse functions are also singularity functions. It is defined as d∂(t)/dt=∂’(t)=0.
9. What is the area under a doublet function?
Explanation: We can explain by-
Integration -infinity to +infinity x(t)∂’(t)dt= negative of Integration -infinity to +infinity x’(t)∂’(t)dt=-x’(t)|t=0=-X’(0), where x(t) is any continuous function having a continuous derivative at t=0. This is ∫∂’(t)=0.
10. How are discrete unit impulse functions and discrete time unit step functions related?
a) They are inverse of each other
d) Integration of unit step function gives unit step function.
Explanation: From definition of u(n) and u(n-1),
u(n) – u(n-1)=∂(n)+sigma k=1 to infinity∂(n-k)- sigma k=1 to infinity ∂(n-k) = ∂(n). In continuous time, ∂(t)=du(t)/dt.
Sanfoundry Global Education & Learning Series – Signals & Systems.
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