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Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE) PDF Download

Q1: If the energy of a continuous-time signal x(t) is E and the energy of the signal 2x(2t − 1) is cE, then c is ______ (rounded off to 1 decimal place).      (2024)
(a) 1.2
(b) 2
(c) 2.6
(d) 3.2
Ans:
(b)
Sol: Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)
Q2: Consider the discrete-time system T1 and T2 defined as follows:
Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)Which one of the following statement is true?     (2024)
(a) 𝑇1T1 and T2 are BIBO stable.
(b) T1 and T2 are not BIBO stable.
(c) T1 is BIBO stable butT2 is not BIBO stable.
(d) T1 is not BIBO stable but T2 is BIBO stable.  
Ans: 
(d)
Sol: Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)Let,
Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)Let,
Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)T1 is not BIBO stable but T2 is BIBO stable.

Q3: Suppose signal y(t) is obtained by the time-reversal of signal x(t), i.e.,  y(t) = x(−t), -∞
ltt
lt∞. Which one of the following options is always true for the convolution of x(t) and y(t) ?       (2024)
(a) It is an even signal.
(b) It is an odd signal.
(c) It is a causal signal.
(d) It is an anti-causal signal.
Ans:
(a)
Sol: Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)even function.

Q4: The period of the discrete-time signal x[n] described by the equation below is N = ___ (Round off to the nearest integer).     (2023)
Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)(a) 16
(b) 32
(c) 48
(d) 64
Ans: 
(c)
Sol: Given :
Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)
Q5: For the signals x(t) and y(t) shown in the figure, z(t) = x(t) ∗ y(t) is maximum at t = T1. Then T1 in seconds is (Round off to the nearest integer).       (2023)
Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)(a) 2
(b) 3
(c) 4
(d) 5
Ans:
(c)
Sol: Using convotution property
z(t) = x(t) ∗ y(t)
Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)For max. overlap
Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)
Q6: Two discrete-time linear time-invariant systems with impulse responses h1[n] = δ[n − 1] + δ[n + 1] and  h2[n] = δ[n] + δ[n − 1] are connected in cascade, where δ[n] is the Kronecker delta. The impulse response of the cascaded system is       (2021)
(a) 𝛿[𝑛2]+𝛿[𝑛+1]δ[n − 2] + δ[n + 1]
(b) 𝛿[𝑛1]𝛿[𝑛]+𝛿[𝑛+1]𝛿[𝑛1]δ[n − 1]δ[n] + δ[n + 1]δ[n − 1]
(c) δ[n − 2] + δ[n − 1] + δ[n] + δ[n + 1]
(d) δ[n] δ[n − 1] + δ[n − 2] δ[n + 1]
Ans: 
(c)
Sol: Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)By applying z -transform
Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)By applying inverse ZT,
Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)
Q7: Suppose for input x(t) a linear time-invariant system with impulse response h(t) produces output y(t), so that x(t) ∗ h(t) = y(t). Further, if  x(t)∣ ∗ ∣h(t)∣ = z(t), which of the following statements is true?         (2020)
(a) For all t ∈ (−∞, ∞), z(t) ≤ y(t)
(b) For some but not all t ∈ (−∞, ∞), z(t) ≤ y(t)  
(c) For all t ∈ (−∞, ∞), z(t) ≥ y(t)
(d) For some but not all t ∈ (−∞, ∞), z(t) ≥ y(t)
Ans: 
(c)
Sol: Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)Case-1:
Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)case 2:
Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)then, y(t) = z(t)
Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)Thus, z(t) ≥ y(t), for all ’t’ .

Q8: The symbols, a and T, represent positive quantities, and u(t) is the unit step function. Which one of the following impulse responses is NOT the output of a causal linear time-invariant system?      (2019)
(a) 𝑒+𝑎𝑡𝑢(𝑡)e+atu(t)
(b) 𝑒𝑎(𝑡+𝑇)𝑢(𝑡)e−a(t+T)u(t)
(c) 1+𝑒𝑎𝑡𝑢(𝑡)1+e−atu(t)
(d) e−a(t−T)u(t)
Ans:
(c)
Sol: a and T represents positive quantities.
u(t) is unit step function.
h(t) = 1+e−atu(t), is non-causal
Here '1' is a constant and two sided so the system will be non-causal, because for causal system,
Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)
Q9: The signal energy of the continuous-time signal x(t) = [(t − 1)u(t − 1)] − [(t − 2)u(t − 2)] − [(t − 3)u(t − 3)] + [(t − 4)u(t − 4)] is     (2018)
(a) 11/3
(b) 7/3
(c) 1/3
(d) 5/3
Ans: 
(d)
Sol: x(t) = r(t − 1) − r(t − 2) − r(t − 3) + r(t − 4)
Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)
Q10: The mean square value of the given periodic waveform f(t) is_________      (SET-2 (2017))
Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)(a) 12
(b) 24
(c) 6
(d) 3
Ans:
(c)
Sol: Mean square value = power of f(t)
Mean square value
Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)
Q11: Consider the system with following input-output relation y[n] = (1 + (−1)n)x[n] where, x[n] is the input and y[n] is the output. The system is       (SET-1 (2017))
(a) invertible and time invariant
(b) invertible and time varying
(c) non-invertible and time invariant
(d) non-invertible and time varying
Ans:
(d)
Sol: Given relationship,
y(n) = [1+(−1)n]x(n)
Time invariance test: 
Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)Since, y(n−1) ≠ y′(n)
So, the system is time invariant.
Invertibility test:
Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)Thus, we are getting many to one mapping between input and output. So, the system is non-invertible.

Q12: The value of Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE) is the Dirac delta function, is     (SET-1  (2016))
(a) 1/2e
(b) 2/e
(c) 1/e2
(d) 1/2e2
Ans:
(a)
Sol: To find the value of Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)
Since, Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE) above integral can be written as
Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)
Q13: The function shown in the figure can be represented as     (SET-1 (2014))
Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)(a) Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)

(b) Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)
(c) Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)
(d) Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)
Ans: (a)
Sol: Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)The given function can be realized as follow:
Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)Combining the function (i0, (ii), (iii) and (iv), we get the given function
Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)Therefore,
Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)
Q14: A zero mean random signal is uniformly distributed between limits -a and +a and its mean square value is equal to its variance. Then the r.m.s value of the signal is      (2011)
(a) a/√3
(b) a/√2
(c) a√2
(d) a√3
Ans:
(a)

Q15: Given a sequence x[n], to generate the sequence y[n] = x[3 - 4n], which one of the following procedures would be correct ?      (2008)
(a) First delay x[n] by 3 samples to generate z1[n], then pick every 4th sample of z1[n] to generate z2[n], and than finally time reverse  z2[n] to obtain y[n].
(b) First advance x[n] by 3 samples to generate z1[n], then pick every 4th sample of z1[n] to generate z2[n], and then finally time reverse  z2[n] to obtain y[n]
(c) First pick every fourth sample of x[n] to generate v1[n], time-reverse v1[n] to obtain v2[n], and finally advance v2[n] by 3 samples to obtain y[n]
(d) First pick every fourth sample of x[n] to generate v1[n], time-reverse v1[n] to obtain v2[n], and finally delay v2[n] by 3 samples to obtain y[n]
Ans: 
(b)
Sol: y[n] = x[3 − 4n] = x[−4n + 3]
So to obtain y[n], we first advance x[n] by 3 unit.
i.e. z1[n] = x[n + 3]
Now we will take every fourth sample of z1[n]
i.e. z2[n] = z1[4n] = x[4n + 3]
Now reverse (time reverse) z2[n] will give
 y[n] = z2[−n] = x[−4n + 3]

Q16: A continuous-time system is described by y(t) = e−∣x(t)∣, where y(t) is the output and x(t) is the input. y(t) is bounded      (2006)
(a) only when x(t) is bounded
(b) only when x(t) is non-negative
(c) only for t ≥ 0 if x(t) is bounded for t ≥ 0
(d) even when x(t) is not bounded
Ans:
(d)

Q17: Which of the following is true?      (2006)
(a) A finite signal is always time bounded
(b) A time bounded signal always possesses finite energy
(c) A bounded signal is always zero outside the interval [−t0, t0 ] for some t0
(d) A time bounded signal is always finite
Ans:
(d)

Q18: What is the rms value of the voltage waveform shown in figure?     (2002)
Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)(a) (200/π) V

(b) (100/π) V
(c) 200V
(d) 100V
Ans: 
(d)
Sol: RMS value
Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)
Q19: A current impulse 5δ(t), is forced through a capacitor C. The voltage Vc(t), across the capacitor is given by       (2002)
(a) 5t
(b) 5u(t) - C
(c) (5/C) (t)
(d) 5u(t)/C
Ans:
(d)
Sol: Previous Year Questions- Introduction of C.T. and D.T. Signals | Signals and Systems - Electrical Engineering (EE)

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FAQs on Previous Year Questions- Introduction of C.T. and D.T. Signals - Signals and Systems - Electrical Engineering (EE)

1. What is the difference between continuous-time (C.T.) and discrete-time (D.T.) signals?
Ans. Continuous-time signals are defined for all values of time, while discrete-time signals are defined only at specific time instances.
2. How are continuous-time signals represented mathematically compared to discrete-time signals?
Ans. Continuous-time signals are represented by mathematical functions of time, while discrete-time signals are represented by sequences of values at discrete time instances.
3. Can continuous-time signals be converted to discrete-time signals and vice versa?
Ans. Yes, continuous-time signals can be sampled to obtain discrete-time signals, and discrete-time signals can be interpolated to obtain continuous-time signals.
4. What are some examples of continuous-time and discrete-time signals commonly encountered in electrical engineering?
Ans. Examples of continuous-time signals include sine waves, cosine waves, and exponential functions. Examples of discrete-time signals include sequences of numbers such as digital audio samples or sensor readings.
5. How are continuous-time and discrete-time signals processed differently in signal processing applications?
Ans. Continuous-time signals are typically processed using analog signal processing techniques, while discrete-time signals are processed using digital signal processing techniques involving sampling, quantization, and filtering.
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