Signals And Systems Set 1

Electrical Engineering

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This set of Signals and Systems Multiple Choice Questions & Answers (MCQs) focuses on Signals And Systems Set 1

Q1 | Evaluate the following function in terms of t: {integral from 0 to t}{Integral from -inf to inf}d(t)
  • 1⁄t
  • 1⁄t2
  • t
  • t2
Answer: t
Explaination:
the first integral is 1, and the overall integral evaluates to t.
Q2 | The fundamental period of exp(jwt) is
  • pi/w
  • 2pi/w
  • 3pi/w
  • 4pi/w
Answer: 2pi/w
Explaination:
the function assumes the same value after t+2pi/w, hence the period would be 2pi/w.
Q3 | Find the magnitude of exp(jwt). Find the boundness of sin(t) and cos(t).
  • 1, [-1,2], [-1,2]
  • 0.5, [-1,1], [-1,1]
  • 1, [-1,1], [-1,2]
  • 1, [-1,1], [-1,1]
Answer: 1, [-1,1], [-1,1]
Explaination:
the sin(t)and cos(t) can be found using euler’s rule.
Q4 | Find the value of {sum from -inf to inf} exp(jwn)*d[n].
  • 0
  • 1
  • 2
  • 3
Answer: 1
Explaination:
the sum will exist only for n = 0, for which the product will be 1.
Q5 | Compute d[n]d[n-1] + d[n-1]d[n-2] for n = 0, 1, 2.
  • 0, 1, 2
  • 0, 0, 1
  • 1, 0, 0
  • 0, 0, 0
Answer: 0, 0, 0
Explaination:
only one of the values can be one at a time, others will be forced to zero, due to the delta function.
Q6 | Defining u(t), r(t) and s(t) in their standard ways, are their derivatives defined at t = 0?
  • yes, yes, no
  • no, yes, no
  • no, no, yes
  • no, no, no
Answer: no, no, no
Explaination:
none of the derivatives are defined at t=0.
Q7 | Which is the correct Euler expression?
  • exp(2jt) = cos(2t) + jsin(t)
  • exp(2jt) = cos(2t) + jsin(2t)
  • exp(2jt) = cos(2t) + sin(t)
  • exp(2jt) = jcos(2t) + jsin(t)
Answer: exp(2jt) = cos(2t) + jsin(2t)
Explaination:
euler rule: exp(jt) = cos(t) + jsin(t).
Q8 | The range for unit step function for u(t – a), is                  
  • t < a
  • t ≤ a
  • t = a
  • t ≥ a
Answer: t ≥ a
Explaination:
a unit step signal u(t) = 1 when t ≥ 0 and 0 when t < 0
Q9 | Which one of the following is not a ramp function?
  • r(t) = t when t ≥ 0
  • r(t) = 0 when t < 0
  • r(t) = ∫u(t)dt when t < 0
  • r(t) = du(t)⁄dt
Answer: r(t) = du(t)⁄dt
Explaination:
ramp function r(t) = t when t ≥ 0 and r(t) = 0 when t < 0
Q10 | Unit Impulse function is obtained by using the limiting process on which among the following functions?
  • triangular function
  • rectangular function
  • signum function
  • sinc function
Answer: rectangular function
Explaination:
unit impulse function can be obtained by using a limiting process on the rectangular pulse function. area under the rectangular pulse is equal to unity.
Q11 | When is a complex exponential signal pure DC?
  • σ = 0 and Ω < 0
  • σ < 0 and Ω = 0
  • σ = 0 and Ω = 0
  • σ < 0 and Ω < 0
Answer: σ = 0 and Ω = 0
Explaination:
a complex exponential signal is represented as x(t)= est
Q12 | What is exp(ja) equal to, where j is the square root of unity?
  • cos ja + jsin a
  • sin a + jcos a
  • cos j + a sin j
  • cos a + jsin a
Answer: cos a + jsin a
Explaination:
this is the corollary of demoivre/euler’s theorem.
Q13 | What is the magnitude of exp(2+3j)?
  • exp(2.3)
  • exp(3)
  • exp(2)
  • exp(3/2)
Answer: exp(2)
Explaination:
exp(a+b) =exp(a) * exp(b), and
Q14 | What is the fundamental frequency of exp(2pi*w*j)?
  • 1pi*w
  • 2pi*w
  • w
  • 2w
Answer: w
Explaination:
fundamental period = 2pi/w, hence fundamental frequency will be w.
Q15 | Total energy possessed by a signal exp(jwt) is?
  • 2pi/w
  • pi/w
  • pi/2w
  • 2pi/3w
Answer: 2pi/w
Explaination:
energy possessed by a periodic signal is the integral of the square of the magnitude of the signal over a time period.
Q16 | Sinusoidal signals multiplied by decaying exponentials are referred to as
  • amplified sinusoids
  • neutralized sinusoids
  • buffered sinusoids
  • damped sinusoids
Answer: damped sinusoids
Explaination:
the decaying exponentials
Q17 | What is the period of exp(2+pi*j/4)t?
  • 4
  • 8
  • 16
  • 20
Answer: 8
Explaination:
the fundamental period = 2pi/(pi/4) = 8.
Q18 | exp(jwt) is periodic
  • for any w
  • for any t
  • for no w
  • for no t
Answer: for any w
Explaination:
any two instants, t and t + 2pi will be equal, hence the signal will be periodic with period 2pi.
Q19 | Define the fundamental period of the following signal x[n] = exp(2pi*j*n/3) + exp(3*pi*j*n/4)?
  • 8
  • 12
  • 18
  • 24
Answer: 24
Explaination:
the first signal, will repeat itself after 3 cycles. the second will repeat itself after 8 cycles. thus, both of them
Q20 | exp[jwn] is periodic
  • for any w
  • for any t
  • for w=2pi*m/n
  • for t = 1/w
Answer: for w=2pi*m/n
Explaination:
discrete exponentials are periodic only for a particular choice of the fundamental frequency.
Q21 | The most general form of complex exponential function is:
  • eσt
  • eΩt
  • est
  • eat
Answer: est
Explaination:
the general form of complex exponential function is: x(t) = est where s = σ
Q22 | A complex exponential signal is a decaying exponential signal when
  • Ω = 0 and σ > 0
  • Ω = 0 and σ = 0
  • Ω ≠ 0 and σ < 0
  • Ω = 0 and σ < 0
Answer: Ω = 0 and σ < 0
Explaination:
let x(t) be the complex exponential signal
Q23 | When is a complex exponential signal sinusoidal?
  • σ =0 and Ω = 0
  • σ < 0 and Ω = 0
  • σ = 0 and Ω ≠ 0
  • σ ≠ 0 and Ω ≠ 0
Answer: σ = 0 and Ω ≠ 0
Explaination:
a signal is sinusoidal when σ = 0 and Ω ≠ 0
Q24 | An exponentially growing sinusoidal signal is:
  • σ = 0 and Ω = 0
  • σ > 0 and Ω ≠ 0
  • σ < 0 and Ω ≠ 0
  • σ = 0 and Ω ≠ 0
Answer: σ > 0 and Ω ≠ 0
Explaination:
a complex exponential signal is sinusoidal when Ω has a definite value i.e., Ω ≠ 0. it can either be growing exponential or decaying exponential based on the value of σ.
Q25 | Determine the nature of the signal: x(t) = e-0.2t [cosΩt + jsinΩt].
  • exponentially decaying sinusoidal signal
  • exponentially growing sinusoidal signal
  • sinusoidal signal
  • exponential signal
Answer: exponentially decaying sinusoidal signal
Explaination:
clearly the signal has negative exponential ⇒ decaying exponential signal. the signal also has sinusoidal component.
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