178 + Interview Questions in Signals and Systems in Electronics and Communication Engineering Page 1 InterviewSolution

1.	What about the stability of system in
Answer» ROC include the unit circle hence it is stable.

Discussion

2.	Which one most appropriate dynamic system?
Answer» Because present output of y(n) depend upon past y(n - 1) and future y(n + 1).

Discussion

3.	An energy signal has G() = 10. Its energy density spectrum is
Answer» Energy density spectrum = \|G(f)\|2 = \|10\|2 = 100.

Discussion

4.	Consider Pole zero diagram as shown, If two Poles are moved in opposite direction towards ω = /2 and -/2, the filter will be
Answer» But still we will get the same response, zero are at same position.

Discussion

5.	If otherwise find E(X)
Answer» .

Discussion

6.	The data of speed of train V and resistance to motion R isThe law R = a + bV is of the form
Answer» Use method of least squares.

Discussion

7.	The function δ( - ) is
Answer» δ(t) is an impulse at t = 0, δ(t - b) is in impulse originating at t = b.

Discussion

8.	If () and its first derivative are Laplace transformable and Laplace of transform () is X(), then () is
Answer» It is initial value theorem.

Discussion

9.	If a function has only cosine terms, it must satisfy the equation
Answer» cos (- θ) = cos θ.

Discussion

10.	If () is a time varying voltage, is
Answer» Since .

Discussion

11.	An ac network has a power factor of 0.8 lagging for fundamental frequency. If the applied voltage contains thrid and fifth harmonics, the overall power factor will be
Answer» As frequency increases, XL decreases and power factor becomes worse.

Discussion

12.	what will be sampling rate to aviod aliasing for the signal m() = 10 cos 100 ?
Answer» To avoid aliasing fs ≤ 2fm .

Discussion

13.	If Laplace transform of () is F(), then =
Answer» £f(t) = £-1F(s) = f(t) £[a f1(t) + bf2(t)] = aF1(s) + bF2(s) where £[f(t - T)] = e-sT F(s) £[e-at f(t)] = F(s + a) Initial value theorem Final value theroem Convolution Integral where t is dummy variable for t.

Discussion

14.	Choose the function (), - ∞ < < + ∞, for which a Fourier series cannot be defined
Answer» Fourier series is applicable for periodic or finite duration signal and (c) is neither periodic nor finite duration signal.

Discussion

15.	If then the sequence [] is
Answer» Therefore x[n] is not periodic.

Discussion

16.	A 1 kHz sinusoidal signal is ideally sampled at 1500 samples/sec and the sampled signal is passed through an ideal low pass filter with cut off frequency 800 Hz. The output signal has the frequency.
Answer» Given fs = 1500 Hz &Rightarrow; fm = 750 Hz. The given signal frequency is 1 kHz. The sampled frequency is 2.5 kHz, 0.5 kHz, But cut off frequency is 800 Hz or 0.8 kHz. Therefore only 0.5 kHz will pass.

Discussion

17.	If autocorrelation sequence is R() = then what will be energy of sequence?
Answer» In autocorrelation sequence max. energy lies at origin.

Discussion

18.	If I() = , fnal value of () is
Answer» .

Discussion

19.	If sequence () = (-) then it is
Answer» If n is +ve then causal, and if n is -ve then non-causal.

Discussion

20.	In the given figure 15.6 shows a series, R - C circuit fed by a current source (). There is an initial voltage . across the capacitor. The system
Answer» Due to presence of v0 the response will not proportional to cause. Hence v0 must be zero if it is a linear system.

Discussion

21.	Fourier transform of an external exponential W0
Answer» Eternal mean the range is -∞ to +∞ So F[ejω0t] = =δ(f - f0).

Discussion

22.	If = 10 + 12 cos 500 - 3.5 sin 500 , then in amplitude phasse form =
Answer» Use trigonometric theorem.

Discussion

23.	The real part of complex frequency corresponds to oscillations.
Answer» The real part of s corresponds to change in amplitude.

Discussion

24.	A voltage = 100 sin ω + 10 sin 5 ω is applied to a pure capacitor having capacitance of 1 μF. If ω = 314 rad/sec, the current through the capacitor is
Answer» For Fundamental .

Discussion

25.	The F.T. of a conjugate symmetric function is always
Answer» F.T. of conjugate symmetric function is always real.

Discussion

26.	Which one is time invariant system?
Answer» For time invariant system y(n, k) = y(n - k), where y(n, k) mean shift the input by n - k, while y(n - k) mean change all the n (a) y[n] = x[2n] &Rightarrow; y(n, k) = x[2n - k] y(n - k) = x[2(n - k)] y(n, k) ≠ y(n - k) Time variant (b) y[n] = x[n] x[n - 1] y[n, k] = x[n - k] x[n - k - 1] y[n - k] = x[n - k] x[n - k - 1] y[n, k] = x[n - k] Time Invariant (c) y[n] = x[n/2] &Rightarrow; y[n, k] &Rightarrow; y[n - k] y[n, k] ≠ y[n - k] Time variant.

Discussion

27.	The Fourier series representation of a periodic current (2 + 6 cos ω + sin 2ω) A. The effective value is
Answer» I =(22 + 62 + 24)0.5 = 64 = 8.

Discussion

28.	Energy density spectrum of a gate G() function is
Answer» and E.S.D. of g(t) = \|G(f)\|2 So E.S.D. of GT(t) = \|G(f)\|2 .

Discussion

29.	If , then () series has
Answer» Use power series method to solve it.

Discussion

30.	DTFT (Discrete time Fourier transform) of [] = ∪[] for -1 < < + 1.
Answer» .

Discussion

31.	The - transform of a systerm is If the ROC is \|\| < 0.2, then the impluse response of the system is
Answer» ROC is \|z\| < 0.2, which shows x(n) must be non-causal, therefore sequence must be left handed. But given is z-transform of right handed sequence. But if H(z) become then ROC become \|z\| < 0.2 and inverse z-transform of is - (0.2)n ∪(- n - 1).

Discussion

32.	ROC of sequence [] = (3) ∪[] + (4) ∪[- - 1]
Answer» x[n] = (3)n ∪(n) + (4)n ∪(- n - 1)

Discussion

33.	δ( - ) is a pulse function.
Answer» It is an impulse function occuring at t = b.

Discussion

34.	If () is in volts, then F(ω) is in
Answer» Since we integrate with respect to time to F(jω), we get volt-secs.

Discussion

35.	A voltage V() which is a Gaussian ergodic random process with a mean of zero and a variance of 4 volt is measured by a true rms meter. The reading will be
Answer» Rms Uvalue =4.

Discussion

36.	An ac circuit has an impedance of (3 + 6) ohm for fundamental. The impedance for fifth harmonic is
Answer» R is independent of w and XL ∝ ω.

Discussion

37.	If then, (0) and (∞) are given by
Answer» Use initial and final value theorems.

Discussion

38.	The signal define by the equations( -) = 0 for < and ( - ) = 1 for ≥ is
Answer» u(t) is a unit step function u(t - a) is a unit step function shifted in time by a.

Discussion

39.	A signal is sampled at Nyquist rate = 2. The function can be recovered from its samples only. If it is a
Answer» Nyqist theorem is defined with respect to sinusoidal signal.

Discussion

40.	A voltage wave is = 50 sin ω. Its average value calculated over full one cycle is
Answer» Average of sinusoid over full cycle is zero.

Discussion

41.	If () and () are two functions of time and and are constants, then
Answer» £f(t) = £-1F(s) = f(t) £[a f1(t) + bf2(t)] = aF1(s) + bF2(s) where £[f(t - T)] = e-sT F(s) £[e-at f(t)] = F(s + a) Initial value theorem Final value theroem Convolution Integral where t is dummy variable for t.

Discussion

42.	The transform of () = ∪()
Answer» .

Discussion

43.	Fourier transform of () =
Answer» It is differentiational Property of F.T. .

Discussion

44.	For the system in the given figure
Answer» yk has two unit delays and then a multiplier of 0.5 before being fedback.

Discussion

45.	The Laplace transform of the waveform shown in the below figure is
Answer» x(t) = ∪(t - 1) + ∪(t - 2) - 2∪(t - 3).

Discussion

46.	A signal () = sin(ω + φ) is the input to a linear time invariant system having a frequency response H() If the O/P of the system is A( -), then the general form of H() will be
Answer» y(n) = A x(n - n0) &Rightarrow; A sin (ω0(n - n0) + Φ) &Rightarrow; A sin (ω0 n - n0ω0 + Φ) and ∠4 (ejω) is - n0ω0 + 2pk.

Discussion

47.	If then system is
Answer» ROC will be \|z\| > 0.4 and \|z\| > 2 Hence ROC &Rightarrow; \|z\| > 0.4, which is exterior of circle of radius 0.4 Hence causal if ROC is \|z\| > 0.4 then non-causal.

Discussion

48.	A pulse function having magnitude E and duration from = 0 to = can be represented as
Answer» v(t) = Eu(t) - Eu(t - a).

Discussion

49.	If , =
Answer» .

Discussion

50.	If I() = , initial value of () is
Answer» .

Discussion

Explore topic-wise InterviewSolutions in .

What about the stability of system in

Which one most appropriate dynamic system?

An energy signal has G() = 10. Its energy density spectrum is

Consider Pole zero diagram as shown, If two Poles are moved in opposite direction towards ω = /2 and -/2, the filter will be

If otherwise find E(X)

The data of speed of train V and resistance to motion R isThe law R = a + bV is of the form

The function δ( - ) is

If () and its first derivative are Laplace transformable and Laplace of transform () is X(), then () is

If a function has only cosine terms, it must satisfy the equation

If () is a time varying voltage, is

An ac network has a power factor of 0.8 lagging for fundamental frequency. If the applied voltage contains thrid and fifth harmonics, the overall power factor will be

what will be sampling rate to aviod aliasing for the signal m() = 10 cos 100 ?

If Laplace transform of () is F(), then =

Choose the function (), - ∞ < < + ∞, for which a Fourier series cannot be defined

If then the sequence [] is

A 1 kHz sinusoidal signal is ideally sampled at 1500 samples/sec and the sampled signal is passed through an ideal low pass filter with cut off frequency 800 Hz. The output signal has the frequency.

If autocorrelation sequence is R() = then what will be energy of sequence?

If I() = , fnal value of () is

If sequence () = (-) then it is

In the given figure 15.6 shows a series, R - C circuit fed by a current source (). There is an initial voltage . across the capacitor. The system

Fourier transform of an external exponential W0

If = 10 + 12 cos 500 - 3.5 sin 500 , then in amplitude phasse form =

The real part of complex frequency corresponds to oscillations.

A voltage = 100 sin ω + 10 sin 5 ω is applied to a pure capacitor having capacitance of 1 μF. If ω = 314 rad/sec, the current through the capacitor is

The F.T. of a conjugate symmetric function is always

Which one is time invariant system?

The Fourier series representation of a periodic current (2 + 6 cos ω + sin 2ω) A. The effective value is

Energy density spectrum of a gate G() function is

If , then () series has

DTFT (Discrete time Fourier transform) of [] = ∪[] for -1 < < + 1.

The - transform of a systerm is If the ROC is || < 0.2, then the impluse response of the system is

ROC of sequence [] = (3) ∪[] + (4) ∪[- - 1]

δ( - ) is a pulse function.

If () is in volts, then F(ω) is in

A voltage V() which is a Gaussian ergodic random process with a mean of zero and a variance of 4 volt is measured by a true rms meter. The reading will be

An ac circuit has an impedance of (3 + 6) ohm for fundamental. The impedance for fifth harmonic is

If then, (0) and (∞) are given by

The signal define by the equations( -) = 0 for < and ( - ) = 1 for ≥ is

A signal is sampled at Nyquist rate = 2. The function can be recovered from its samples only. If it is a

A voltage wave is = 50 sin ω. Its average value calculated over full one cycle is

If () and () are two functions of time and and are constants, then

The transform of () = ∪()

Fourier transform of () =

For the system in the given figure

The Laplace transform of the waveform shown in the below figure is

A signal () = sin(ω + φ) is the input to a linear time invariant system having a frequency response H() If the O/P of the system is A( -), then the general form of H() will be

If then system is

A pulse function having magnitude E and duration from = 0 to = can be represented as

If , =

If I() = , initial value of () is