SIGNALS & SYSTEMS (SS)

SP.1) Which among the following is a linear system ?
(a)$ y[n] = x[n] x[n-1]$
(b)$ y[n] = x[n] + x[n-10]$
(c)$ y[n] = x^2[n]$
(d) both (a) & (c)




SP.2) The impulse response of a system is h(t) = t u(t) . For an input  u(t-1), the output is
(a)$\frac{t^2 u(t)}{2}$
(b)$\frac{t(t-1)u(t-1)}{2}$
(c)$\frac{(t-1)^2 u(t-1)}{2}$
(d)$\frac{(t^2 - 1)u(t-1)}{2}$




SP.3) The impulse response of a continuous time system is given by  h(t) =  δ(t-1) +  δ(t-3).  The value of step response at t = 2
(a)0
(b)1
(c)2
(d)3



SP.4) Consider an LTI system with Transfer function H(s) =1/s(s+4). 
If the input to the system is cos(3t) and the steady state output is $A sin(3t + \alpha)$ then the value of A is
(a) 1/30
(b) 1/15
(c) 3/4
(d) 4/3





SP.5) For the discrete time system of the given figure:




(a) y(k) - 0.5 y(k-1) - 0.25 y(k-2) = u(k)

(b) y(k) - 0.5 y(k-1) + 0.25 y(k-2) = u(k)
(c) y(k) + 0.5 y(k-1) - 0.25 y(k-2) = u(k)
(d) y(k) + 0.5 y(k-1) + 0.25 y(k-2) = u(k)




SP.6) ROC of the sequence x[n] = a^n u[n] is

(a) z > a
(b) z < a
(c) |z| > a
(d) |z| < a





SP.7) For the analog signal m(t) = 4 cos(100πt) + 8 sin(200πt) + cos(300πt) , the Nyquist Sampling Rate will be
(a) 1/100
(b) 1/200
(c) 1/300
(d) 1/600



Explanation
Nyquist Sampling frequency must be the twice the highest message frequency in the signal. 
Further, Nyquist Sampling rate is the reciprocal of Nyquist Sampling frequency. 
Thus Nyquist sampling rate = 1/(2*150) = 1/300. Here 150 is the highest frequency of the signal m(t) [as evident from cos(300πt) when expressed as cos(2*150*πt).]

SP.8) In Laplace transform, multiplication by e^(-at) in time domain becomes
(a) translation by a in s-domain 
(b) translation by (-a) in s-domain 
(c) multiplication by e^(-as) in s-domain
(d) none of above




SP.9) Inverse Fourier transform of sgn(ω)is

(a) j/πt
(b) 1
(c) u(t)
(d) 2/jt




SP.10) For an input x(t) , the output y(t) of a modulator is given by 

y(t) = x(t) cos(2πft) where f(t) is carrier frequency. The system is
(a) dynamic,nonlinear & time invariant
(b) static,linear & time-variant
(c) static,non-linear & time-variant
(d) dynamic,linear & time-variant




SP.11) A signal m(t) is multiplied by a sinusoidal waveform of a frequency fc such that v(t) = m(t)cos(2π fc t). If Fourier Transform of m(t) is M(f), Fourier Transform of v(t) will be
(a) 0.5 M(f + fc)
(b) 0.5 M(f - fc)
(c) 0.5 M(f + fc) + 0.5 M(f - fc)
(d) 0.5 M(f - fc) + 0.5 M(f - fc)
Answer is (c)

SP.12) For a periodic signal v(t) = 30 sin (100t) + 10 cos 300t + 6 sin (500+π/4), the fundamental frequency in rad/s
(a) 100
(b) 300
(c) 500
(d) 1500
Answer is (a)

SP.13) For the function x(t) shown in figure

 even & odd parts of a unit step function u(t) are respectively
(a) 0.5,0.5 x(t)
(b) -0.5,0.5 x(t)
(c) 0.5,-0.5 x(t)
(d) -0.5,-0.5 x(t)
Answer is (a)


SP.14) The following is true
(a) A Finite Signal is Always Bounded
(b) A Bounded Signal Always possess Finite Energy
(c) A Bounded Signal is Zero outside the interval [-t0,t0] for some t0
(d) A Bounded Signal is Always Finite
Answer is (b)

SP.15) Which type of programming is typically used for digital signal processors?
(a) Assembly language
(b) Machine language
(c) C
(d) None of the above
Answer is (a)

SP.16)Which Filters have the characteristic to be best suited for filtering pulse waveforms
(a)Butterworth
(b)Chebhyshev
(c)Bessel
(d) none of above
Answer is (c)
SP.17) Which of the following is the first method proposed for design of FIR filters?
(a) Chebyshev approximation
(b) Frequency sampling method
(c) Windowing technique
(d) None of these
Answer is (c)

SP.18)For an N-point FFT algorithm with N=2^m , which one of the following statement is TRUE?
(a)It is not possible to construct a signal flow graph with both input and output in normal order
(b)The number of butterflies in the m-th state is N/m
(c)In-place computation requires storage of only 2N node data
(d)Computation of a butterfly requires only one complex multiplication
Answer is (d)

SP.19)The correct expression for transition band Δf is
(a) (ωp- ωs)/2π
(b) (ωp+ωs)/2π
(c) (ωp.ωs)/2π
(d) (ωs- ωp)/2π
Answer is (d)

SP.20) Which of the following condition is true?
(a)$ N \geq \frac{\log\frac{1}{k}}{\log\frac{1}{d}}$
(b)$ N \geq \frac{\log k}{\log d}$
(c)$ N \geq \frac{\log d}{\log k}$
(d)$ N \geq \frac{\log\frac{1}{d}}{\log\frac{1}{k}}$
Answer is (d)

SP.21) Which of the following defines a chebyshev polynomial of order N, Tn(x)?
(a) cos(Ncos-1x) for all x
(b) cosh(Ncosh-1x) for all x
(c) cos(Ncos-1x), |x|≤1
 cosh(Ncosh-1x), |x|>1
(d) None of these

Answer is (c)

SP.22) Two rectangular waveform of duration T1 and T2 seconds are convolved.What is the shape of resulting waveform?
(a) Triangular
(b) Rectangular
(c) Trapezoidal
(d) semi-circular
Answer is (a)

SP.23) The impulse response of an LTI system is a rectangular pulse of duration T.It is excited by an input of a pulse duration T.What is the filter output waveform?
(a) Rectangular pulse of duration T
(b) Rectangular pulse of duration 2T
(c) Triangular pulse of duration T
(d) Triangular pulse of duration 2T
Answer is (c)

SP.24) IIR Filters are
(a) recursive
(b) non-recursive
(c) reversible
(d) non-reversible
Answer is (a)

SP.25) The ROC of z-transform of the discrete time x[n]=(0.5)^|n| is
(a)$ 0.5<|z|<2 $
(b)$ |z|>2$
(c)$-2<|z|<$
(d)$|z|<0.5$
Answer is (a) $x[n] = (0.5)^{|n|}=(0.5)^{n}u[n]+(0.5)^{-n} u[-n-1]$
$x[n]= \sum_{-\infty}^{\infty}x[n]z^{-n}$
$= \sum_{-\infty}^{\infty}(0.5)^{-n}z^{-n}u[-n-1] + \sum_{-\infty}^{\infty}(0.5)^{n}z^{-n}u[n]$
$= \sum_{-\infty}^{-1}(0.5)^{-n}z^{-n} + \sum_{0}^{\infty}(0.5)^{n}z^{-n}$
$= \sum_{1}^{\infty}(0.5)^{n}z^{n} + \sum_{0}^{\infty}(0.5)^{n}z^{-n}$
$= \frac{0.5z}{1-0.5z}+\frac{1}{1-0.5z^{-1}}$
I st term converges only if $|0 .5z|< 1 or |z|<2$
II nd term converges only if $|0.5z^{-1}|<1 or |z|>1/2$


SP.26) Transition band is more in
(a) Butterworth filter
(b) Chebyshev type I
(c) Chebyshev type II
(d) FIR filter
Answer is (a)

SP.27) What is the value of Chebyshev Polynomial of degree 3 ?
(a)$3x^{3}+4x$
(b)$3x^{3}-4x$
(c)$4x^{3}+3x$
(d)$4x^{3}-3x$
Answer is (d)

SP.28) The Fourier Transform of signal u(t)
(a)$\pi\delta(\omega)$
(b)$\frac{1}{j\omega}$
(c)$\pi\delta(\omega)+\frac{1}{j\omega}$
(d)none of these
Answer is (c)

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