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
Answer
Answer: d [Reason:] 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
Answer
Answer: a [Reason:] 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) t2
d) 1⁄t2
Answer
Answer: b [Reason:] 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) t2
Answer
Answer: c [Reason:] 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
Answer
Answer: b [Reason:] 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].
Answer
Answer: d [Reason:] 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
Answer
Answer: b [Reason:] 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
Answer
Answer: d [Reason:] 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
Answer
Answer: d [Reason:] 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)
Answer
Answer: b [Reason:] Euler rule: exp(jt) = cos(t) + jsin(t).
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