Signal Processing — Part 2 MCQs with Explanations

Differentiating the unit step response is the correct answer to “The impulse response of an LTI system can be obtained by”. This question is standard in competitive examination syllabi for Signal Processing.

Causal but not stable is the correct answer to “A system is defined by its impulse response h(n) = 2 n u(n - 2). The system is”. This question is standard in competitive examination syllabi for Signal Processing.

5, 2 is the correct answer to “A discrete time linear shift-invariant system has an impulse response h[n] with h[0] = 1, h[1] = -1, h[2] = 2, and zero otherwise. The system is given an input sequence x[n] with x[0] = x[2] = 1 and zero otherwise. The number of nonzero samples in the output sequence y[n], and the value of y[2] are, respectively”. This question is standard in competitive examination syllabi for Signal Processing.

$${z \over {z - 5}}$$ and the system is stable is the correct answer to “If the impulse response of a discrete-time system is h[n] = -5 n u[- n - 1], then the system function H(z) is equal to”. This question is standard in competitive examination syllabi for Signal Processing.

Computation of a butterfly requires only one complex multiplication is the correct answer to “For an N-point FFT algorithm with N = 2 m , which one of the following statements is TRUE”. This question is standard in competitive examination syllabi for Signal Processing.

Not periodic is the correct answer to “A discrete-time signal x [n] = sin(π 2 n), n being an integer, is”. This question is standard in competitive examination syllabi for Signal Processing.

ejω0t u(t) is the correct answer to “Which one of the following is an eigen function of the class of all continuous-time, linear, time-invariant systems (u(t) denotes the unit-step function)”. This question is standard in competitive examination syllabi for Signal Processing.

$$jfX\left( f \right)$$ is the correct answer to “The Fourier Transform of a function x(t) is X(f). The Fourier transform of $${{dx\left( t \right)} \over {dt}}$$ will be”. This question is standard in competitive examination syllabi for Signal Processing.

$$x\left( t \right) \in R$$ is the correct answer to “The magnitude and phase of the complex Fourier series coefficient a k of a periodic signal x(t) are shown in the figure. Choose the correct statement from the four choices given. Notation: C is the set of complex number, R is the set of purely real numbers, and P is the set of purely imaginary numbers.”. This question is standard in competitive examination syllabi for Signal Processing.

The entire s-plane is the correct answer to “Let the signal i(t) = 0 outside the interval [T 1 , T 2 ], where T 1 and T 2 are finite. Furthermore, |f(t)| < ∞. The region of convergence (ROC) of the signal's bilateral Laplace transform F(s) is”. This question is standard in competitive examination syllabi for Signal Processing.

$${z \over {z - {a^T}}}$$ is the correct answer to “The z-transform F(z) of the function f(nT) = a nT is”. This question is standard in competitive examination syllabi for Signal Processing.

$$\frac{1}{2},\frac{1}{2}x\left( t \right)$$ is the correct answer to “The function x(t) is shown in the figure. Even and odd parts of a unit-step function u(t) are respectively,”. This question is standard in competitive examination syllabi for Signal Processing.

$$\frac{1}{2},\frac{1}{3}$$ is the correct answer to “For the discrete-time system shown in the figure, the poles of the system transfer function are located at”. This question is standard in competitive examination syllabi for Signal Processing.

Is $${1 \over 3} > \left| z \right| > {1 \over 9}$$ is the correct answer to “Let $$x\left[ n \right] = {\left( { - {1 \over 9}} \right)^n}u\left( n \right) - {\left( { - {1 \over 3}} \right)^n}u\left( { - n - 1} \right).$$ The Region of Convergence (ROC) of the z-transform of x[n]”. This question is standard in competitive examination syllabi for Signal Processing.

y is zero for all sampling frequencies ωs is the correct answer to “An LTI system having transfer function $$\frac{{{s^2} + 1}}{{{s^2} + 2s + 1}}$$ and input x(t) = sin(t + 1) is in steady state. The output is sampled at a rate ω s rad/s to obtain the final output {y(k)}. Which of the following is true”. This question is standard in competitive examination syllabi for Signal Processing.

$${1 \over {\left( {0.5 + j0.25} \right)}}$$ is the correct answer to “Let x[n] = x[-n]. Let X(z) be the z-transform of x[n]. If 0.5 + j0.25 is a zero of X(z), which one of the following must also be a zero of X(z).”. This question is standard in competitive examination syllabi for Signal Processing.

{-4 - j2.5, j2, 4 - j2.5} is the correct answer to “Consider the sequence x[n] = {-4 - j5, 1 + j2, 4} The conjugate antisymmetric part of the sequence is”. This question is standard in competitive examination syllabi for Signal Processing.

$${1 \over 3} < \left| z \right| < {2 \over 3}$$ is the correct answer to “If the region of convergence of x 1 [n] + x 2 [n] is $${1 \over 3} < \left| z \right| < {2 \over 3},$$ then the region of convergence of x 1 [n] - x 2 [n] includes”. This question is standard in competitive examination syllabi for Signal Processing.

Even harmonics is the correct answer to “The Fourier series of an odd periodic function, contains only”. This question is standard in competitive examination syllabi for Signal Processing.

Attenuation of high frequencies in reproduction is the correct answer to “Increased pulse-width in the flat-top sampling, leads to”. This question is standard in competitive examination syllabi for Signal Processing.

-(0.2)nu[- n - 1] is the correct answer to “The z-transform of a system is $$H\left( z \right) = {z \over {z - 0.2}}.$$ If the ROC is |z| < 0.2, then the impulse response of the system is”. This question is standard in competitive examination syllabi for Signal Processing.

$$\delta \left( t \right) = \left\{ {\matrix{ {\infty ,} & {t = 0} \cr {0,} & {{\rm{otherwise}}} \cr } } \right.\,\,{\rm{and}}\,\int\limits_{ - \infty }^\infty {\delta \left( t \right)dt = 1} $$ is the correct answer to “The Dirac-delta function δ(t) is defined as”. This question is standard in competitive examination syllabi for Signal Processing.

$$\int\limits_0^t {h\left( \tau \right)} u\left( {t - \tau } \right)d\tau $$ is the correct answer to “Let h(t) be the impulse response of a linear time invariant system. Then the response of the system for any input u(t) is”. This question is standard in competitive examination syllabi for Signal Processing.

2[1 - e-2t]u(t) is the correct answer to “The response of an initially relaxed linear constant parameter network to a unit impulse applied at t = 0 is 4e -2t u(t). The response of this network to a unit step function will be”. This question is standard in competitive examination syllabi for Signal Processing.

16 is the correct answer to “Consider the signal x(t) = cos(6πt) + sin(8πt), where t is in seconds. The Nyquist sampling rate (in samples/second) for the signal y(t) = x(2t + 5) is”. This question is standard in competitive examination syllabi for Signal Processing.

$$ - 4{e^{{{j\pi n} \over 4}}}$$ is the correct answer to “The impulse response h[n] of a linear time invariant system is given as $$h\left[ n \right] = \left\{ {\matrix{ { - 2\sqrt 2 ,} \cr {4\sqrt 2 ,} \cr {0,} \cr } } \right.\matrix{ {n = 1, - 1} \cr {n = 2, - 2} \cr {{\rm{otherwise}}} \cr } $$ If the input to the above system is the sequence $${e^{{{j\pi n} \over 4}}},$$ the output is”. This question is standard in competitive examination syllabi for Signal Processing.

2, 0 is the correct answer to “If $$F\left( s \right) = L\left[ {f\left( t \right)} \right] = {{2\left( {s + 1} \right)} \over {{s^2} + 4s + 7}}$$ then the initial and final values of f(t) are respectively”. This question is standard in competitive examination syllabi for Signal Processing.

|α| < 2, any value of β is the correct answer to “A causal LTI system is described by the difference equation 2y[n] = αy[n - 2] - 2x|n| - βx[n - 1]. The system is stable only if”. This question is standard in competitive examination syllabi for Signal Processing.

$${1 \over {2\pi }}f\left( { - \omega } \right)$$ is the correct answer to “The function f(t) has the Fourier transform f(ω) The Fourier transform of $$g\left( t \right) = \left( {\int\limits_{ - \infty }^\infty {g\left( t \right){e^{ - j\omega }}dt} } \right)$$ is”. This question is standard in competitive examination syllabi for Signal Processing.

Zero is the correct answer to “The z-transform of a signal is given by $$C\left( z \right) = {1 \over 4}{{{z^{ - 1}}\left( {1 - {z^{ - 4}}} \right)} \over {{{\left( {1 - {z^{ - 1}}} \right)}^2}}}.$$ Its final value is”. This question is standard in competitive examination syllabi for Signal Processing.

Only 1 and 3 are true is the correct answer to “Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let {a k } be the complex Fourier series coefficients of x(t), where k is integer valued. Consider the following statements about x(3t): 1. The complex Fourier series coefficients of x(3t) are {a k } where k is integer valued. 2. The complex Fourier series coefficients of x(3f) are {3a k } where k is integer valued. 3. The fundamental angular frequency of x(3t) is 6π rad/s. For the three statements above, which one of the following is correct”. This question is standard in competitive examination syllabi for Signal Processing.

5 Hz and 15 Hz only is the correct answer to “Let x(t) = cos(10πt) + cos(30πt) be sampled at 20 Hz and reconstructed using an ideal low-pass filter with cut-off frequency of 20 Hz. The frequency/frequencies present in the reconstructed signal is/are”. This question is standard in competitive examination syllabi for Signal Processing.

α1 = α2 = 0; α0 = -α3 is the correct answer to “Consider a four point moving average filter defined by the equation $$y\left[ n \right] = \sum\nolimits_{i = 0}^3 {{a_i}x\left[ {n - i} \right]} .$$ The condition on the filter coefficients that results in a null at zero frequency is”. This question is standard in competitive examination syllabi for Signal Processing.

e-jω [cos2ω + 2cosω + 2] is the correct answer to “The Fourier transform of y(2n) will be”. This question is standard in competitive examination syllabi for Signal Processing.

P and S is the correct answer to “The Fourier series of a real periodic function has only P. Cosine terms if it is even Q. Sine terms if it is even R. Cosine terms if it is odd S. Sine terms if it is odd Which of the above statements are correct”. This question is standard in competitive examination syllabi for Signal Processing.

-j is the correct answer to “For a function g(t), it is given that $$\int\limits_{ - \infty }^{ + \infty } {g\left( t \right){e^{ - j\omega t}}dt = \omega {e^{ - 2{\omega ^2}}}} $$ for any real value $$\omega $$ . If $$y\left( t \right) = \int\limits_{ - \infty }^t {g\left( \tau \right)} d\tau ,\,{\rm{then}}\,\int\limits_{ - \infty }^{ + \infty } {y\left( t \right)} dt$$ is. . . . . . . .”. This question is standard in competitive examination syllabi for Signal Processing.

Is stable is the correct answer to “A linear discrete-time system has the characteristics equation, z 3 - 0.81 z = 0. The system”. This question is standard in competitive examination syllabi for Signal Processing.

$$f$$ has frequency components at 0 and $${1 \over \pi }Hz$$ is the correct answer to “A function is given by f(t) = sin 2 t + cos 2t. Which of the following is true”. This question is standard in competitive examination syllabi for Signal Processing.

$$\frac{{{z^{ - 1}}\left( {1 - 0.6{z^{ - 1}}} \right)}}{{\left( {1 - 0.4{z^{ - 1}}} \right)}}$$ is the correct answer to “Two systems H 1 (z) and H 2 (z) are connected in cascade as shown below. The overall output y(n) is the same as the input x(n) with a one unit delay. The transfer function of the second system H 2 (z) is $$x\left( n \right) \to \boxed{{H_1}\left( z \right) = \frac{{\left( {1 - 0.4{z^{ - 1}}} \right)}}{{\left( {1 - 0.6{z^{ - 1}}} \right)}}} \to \boxed{{H_2}\left( z \right)} \to y\left( n \right)$$”. This question is standard in competitive examination syllabi for Signal Processing.

5δ[n + 2] + 3δ[n] + 4δ[n - 1] is the correct answer to “Consider the z-transform X(z) = 5z 2 + 4z -1 + 3; 0 < |z| < ∞. The inverse z-transform x[n] is”. This question is standard in competitive examination syllabi for Signal Processing.