West Bengal Institute of Technology (WBIT) 2008-6th Sem B.Tech Electronics and Communications Engineering Electronics & Comm ( - ) SIGNAL PROCESSING - Question Paper
' C8/S.TBCH (BCE)/aBM-6/EC-01/08 d
ENGINEERING & MANAGEMENT EXAMINATIONS, JUNE - 2008 DIGITAL SIGNAL PROCESSING SEMESTER- 6
Time : 3 Hours J I Full Marks : 70
(Multiple Choice Tjrpe Questions}
1. Choose the correct alternatives for any ten of the following : 10 x 1 = 10
, 1) The Z-transform of u(n - 1) is
a) 1/(1-Z-1) b) Z/Cl-Z"1)
CZI
. - . ' . i '
c) 1 /[ZQ-Z-1)] d) (1+Z-1).
ii) Considering x as the sampling period, transfer function of a discrete-time integrator employing trapezoidal integration is
m\ ..... ks)
13* Ski)' a
Hi) The transfer function of a system with impulse response h (n) = u (n)- u (n- 1) is,
a) 2 TT1 ,
ci .....~ d) i. CZ!
' (Z-1)(Z*1)
* ' * ' jr
iv) A DTLTI system with impulse response g(n) is BIBO stable if
. a) \9{n)\<oo b) g{n)<
n~ ft*** .
, +40 . ' + '
C) ig,()|<0 d) |g(n)!<l.
n-0 n
ck/B.ncB (BGSi/acH-e/i&aoi/oa 4
vj If x(n) Is a flnlte-duratlon, two-sided sequence. ROC of its Z-transform is entire Z-plane except ,
a) Z0 b) Z - 1 , c) Z = co d) both Z = 0 and Z = . ___
vi) If x(n)* |2, 4, 6, 1 j then x (n - 2) is *
a) |2,4, 6, l} b) |2,4, 6, lj
c) |2, 4, 6, 1, oj d) jo, 2, 4, 6, lj. 1..... 1
vii) If x(n) is a sequence of L samples and h(n) of M samples, the convolution of x(n) and h(n) contains
a) Max (L, M) samples b) L + M - 1 samples
c) L + M - 2 samples d) L + M samples. 1 I
viii) The inverse Z-transform of l/|l-2-1J is
a) u(n) as well as -u (- n - 1) b) u(n) but not u (- n - 1)
c) u(n) as well as u(-n) d) u(-n) but not u(n). _
ix) the Fourier transform of an aperiodic discrete-time sequence is
a) discrete & periodic function of frequency
b) discrete & aperiodic function of frequency
c) continuous & periodic function of frequency
d) continuous & aperiodic function of frequency. 1 1
x) Z-transform of a causal sequence x[n) Is 2/|l-~Z_l j. Then x(0) is equal to
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c) 1 d) 4. |
cs/B.raca (BCB)/BM/sc-floi/oat 5
xi) For a rectangular window of Af samples, width of the main lobe Is
a) 2n/m b) n/m
c) 6n/m d) 4n/m.
xll) If jc(n) jl, 0, 0, lj, the DFT valueX(0) is
a) 2 b) 1 + j
c) 0 d) 1-j.
xlii) Two non-interacting DTLTI systems in cascade have impulse responses gin) and h(n). The impulse response of the combination is
a) g(n) h(n) b) g(n)+h(n)
c) g(n)*h(n) d) [g(n) h(n)].
GROUP-B
(Short Answer Type Questions) '
Answer any three of the following. 3x5=15
Z2 .
2. Find the InverseZ-transform ofX(Z) = ROC : |2|>2.
Z2-3Z+2
3. Find the DFT of a sequence xn -{1, 1, 0, 0}.
4. A DTLTI system with impulse response h(n)-|l, 1, lj is excited by a sequence x(n)m j> 3, 2, lj. Determine the output y(n) of the system.
5. The output y(n) and the input x(n) of a discrete-time system are related by the equation y(n)- e*<n). Determine whether the system is linear, time-invariant and stable
6. A signal x(t)=3cos200nt + 2cos500nt is uniformly sampled at a rate 150 samples/second. Determine the frequency information carried by the sampled version of x(t).
o/a.THH pOQ/snM/rowi/o*
6
GROUP-C (Long Answer Type Questions )
3 x i5 = 45
Answer any three of the following questions.
The output and the input of a recursive DTLTI system are related by the equation j/(n) - -0 ly(n -1)+0 2y(n - 2)+3x(n)+3 6x(n -1)+0 6x{n - 2). Derive and draw the direct form-II structure for realising the system. 5
a)
b)
Derive the sketch the cascade and parallel structures for the system with transfer
2(Z + 2)__________10
function H(Z)-
(Z-0-l){Z+0-5KZ+0-4)
Determine the Impulse response of the system with x(n) as input and y(n) as output shown in figure . below. Impulse responses of the subsystems are /it(n)-(l/3)'lu(n)fft2(n)-(l/2)Fun&/(n)-(l/4)nun. Also determine expression for
12 + 3
frequency response of the system.
9. a) Find the IDFT of the sequence X(K)-6, -2+j2, -2, -2 - j2}-
7
3
5
b) State the "Sampling Theorem",
c) Point out the properties of ROC of Z-transform.
10. a) Design a digital Butterworth filter to satisfy the following constraints ' 0-9<|H(e)|il; 0
Use bilinear transformation. Consider a sampling period of 1 second.
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a/i.nca *ai/mi4/ic4oi/M 7 |
b) An analog filter has transfer function
GKS)--~
' (S+1XS+2)
Discretize the filter to obtain the transfer function of an equivalent discrete time filter by impulse-invariant technique. Consider a sampling frequency of 2 Hz. 5 ' . *.
11. Write short notes on any two of the following: 2x7
i) Mapping of S-plane into Z-plane, .
11) DIF algorithm
Iii) Design of linear phase FIR filter
' I . '
iv) Architecture of digital signal processors.
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| Earning: Approval pending. |
