This set of Signals & Systems Multiple Choice Questions & Answers (MCQs) focuses on “Useful Signals”.

1. What is the value of d[0], such that d[n] is the unit impulse function?

a) 0

b) 0.5

c) 1.5

d) 1

View Answer

Explanation: The unit impulse function has value 1 at n = 0 and zero everywhere else.

2. What is the value of u[1], where u[n] is the unit step function?

a) 1

b) 0.5

c) 0

d) -1

View Answer

Explanation: The unit step function u[n] = 1 for all n>=0, hence u[1] = 1.

3. Evaluate the following function in terms of t: {sum from -1 to infinity:d[n]}/{Integral from 0 to t: u(t)}

a) t

b) ^{1}⁄_{t}

c) t^{2}

d) ^{1}⁄_{t2}

View Answer

Explanation: The numerator evaluates to 1, and the denominator is t, hence the answer is 1/t.

4. Evaluate the following function in terms of t: {integral from 0 to t}{Integral from -inf to inf}d(t)

a) ^{1}⁄_{t}

b) ^{1}⁄_{t2}

c) t

d) t^{2}

View Answer

Explanation: The first integral is 1, and the overall integral evaluates to t.

5. The fundamental period of exp(jwt) is

a) pi/w

b) 2pi/w

c) 3pi/w

d) 4pi/w

View Answer

Explanation: The function assumes the same value after t+2pi/w, hence the period would be 2pi/w.

6. Find the magnitude of exp(jwt). Find the boundness of sin(t) and cos(t).

a) 1, [-1,2], [-1,2].

b) 0.5, [-1,1], [-1,1].

c) 1, [-1,1], [-1,2].

d) 1, [-1,1], [-1,1].

View Answer

Explanation: The sin(t)and cos(t) can be found using Euler’s rule.

7. Find the value of {sum from -inf to inf} exp(jwn)*d[n].

a) 0

b) 1

c) 2

d) 3

View Answer

Explanation: The sum will exist only for n = 0, for which the product will be 1.

8. Compute d[n]d[n-1] + d[n-1]d[n-2] for n = 0, 1, 2.

a) 0, 1, 2

b) 0, 0, 1

c) 1, 0, 0

d) 0, 0, 0

View Answer

Explanation: Only one of the values can be one at a time, others will be forced to zero, due to the delta function.

9. Defining u(t), r(t) and s(t) in their standard ways, are their derivatives defined at t = 0?

a) Yes, Yes, No

b) No, Yes, No

c) No, No, Yes

d) No, No, No

View Answer

Explanation: None of the derivatives are defined at t=0.

10. Which is the correct Euler expression?

a) exp(2jt) = cos(2t) + jsin(t)

b) exp(2jt) = cos(2t) + jsin(2t)

c) exp(2jt) = cos(2t) + sin(t)

d) exp(2jt) = jcos(2t) + jsin(t)

View Answer

Explanation: Euler rule: exp(jt) = cos(t) + jsin(t).

**Sanfoundry Global Education & Learning Series – Signals & Systems.**

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