Download AKTU B-Tech 6th Sem 2015-2016 NEC 011 Digital Signal Processing Question Paper

Download AKTU (Dr. A.P.J. Abdul Kalam Technical University (AKTU), formerly Uttar Pradesh Technical University (UPTU) B-Tech 6th Semester (Sixth Semester) 2015-2016 NEC 011 Digital Signal Processing Question Paper

Printed Pages: 6 NEC-Oll
(Following Paper ID and Roll No. to be ?lled in your
Answer Books)
RonNoITTI l l I FFI
B.TECH.
Theory Examination (SemesteroVI) 2015-16
DIGITAL SIGNAL PROCESSIN G
Time : 3 Hours Max. Marks : 100
Section-A
1. Attempt all parts. All parts carry equal marks. Write
answer of each'part in short. (2X10 = 20)
(a) What is Discrete Time Fourier Transform and How it
is related to Discrete Fourier Transform?
(b) Establish the relation between Z-transform and DFT.
(c) What is zero padding? What are its uses?
((1) Calculate number of multiplications needed in calcu?
I lation of DFT and FFT of 32 point sequence and also
calculate speed improvement factor.
(6) Explain Bit? reversal and In-place computation.
ll) P.T.O.
206/m/240/6000

(t) How an [IR ?lter is different than FIR ?lter? ? ('3) Find Citeular convolution of the following sequences
_ . . . 1 using concentric circle method.
(g) Compute X(O) 1f X(K) lS 4-pomt DFT of the followmg
sequence J 1901) =(1,2,2,1)
x(n) = {1,0, ?l,O}
x n = 1,2,3,
(*0 For the given system ?mction, 2( ) ( 4)
(c) (i) Computer 4-point DFI? of the following sequence
H(z)=(1+z?)(1+:i?z?1 +%z'2 +z?3) ?Sing DIF algorithm
Obtain Cascade realization with minimum number of x(n) = cos?
multipliers.
(i) What is Spectral leakage? Give remedy to this (ii) Show that the same algon'thm b
can e used to
problem. . compute [DFT of X(k) calculated in part (a).
(j) What are the main disadvantages 0f designing DR ?lters (d) Compute the DFT of followin 8 '
. . . . 9 g -pomt ence ?
usmg wmdowmg techmtlue. . 4-point Radix-2 DIT algorithm. seq? usmg
SectiOII-B > x(n) = {2, 2, 2a 2, 1, 1, 1, 1}
2. Attempt any ?ve questions from this section. (10X5=50) . . '
. . (e) Obtam D1rect Form 1, Direct Form H and Parallel
(3) Find thelO-point DFT of the following sequences: Form structures for the followin ?l
g ter
i. x(n) = 6(n)+ 5(n?5)
3 3
y(h)=?y(h?1)+?y(h?2)+iy(h-3 h
it x(n) = u(n) -u(n ? 6) 4 32 64 H4 )+3x(h-D+2x(h?2)
2) . 3 '
( Ww/moo ( ) P'T?O'
206/m/240/6000

(f)
(g)
(11)
Consider the causal linear-shi?-invariant ?lter with
the system ?mction
1+0.87Sz"
(1+ 0.22"1 + 0.9z'z)(1? 0.72?)
H(z) =
Obtain following realizations:
(a) Direct Form II
(b) A cascade of ?rst-order and second?order system
realized in transposed DF 11
(c) A Parallel connection of ?rst?order and second-
order systems realized in DF II (2+4+4)
A ?lter is to be designed with the following desired
frequency response:
Transform the prototype LPF with system function
Qp
s+9p
H LP (s) = into a
(4)
206/3 1 2/240/6000
Attempt any two questions from this section.
3.
(a)
(i) HPF with cut-o?? frequency 0p
(ii) BPF with upper and lower cut-off frequencies ?u
and Q; respectively.
Section-C
(15XZ = 30)
Prove that multiplication of the DFTs of two sequences
is equivalent to the circular convolution of the two se-
quences in the time domain.
(b) If the 10-point DFT of x(n)=5(n)?6(n?1) and
(a)
h(n) = u(n) ? u(n -10) are X(k) and H(k) respectively,
?nd the sequence w(n) that corresponds to the 10-point
inverse DFT of the product H(k).X(k). (7+8)
(i) Compute 4-point DFI? of the following sequence using
linear transformation matrix
x(n) = (1, 1?2, ?2)
(ii) Find IDFT x(n) from X(k) calculated in part(i).
(2.5 X2=05)
(5) P.T.O.
20M240/6000

(b) Use Radix-Z DIT algorithm for ef?cient computation
of 8-point DFT of x(n) = 2?. (10)
(a) An FIR ?lter has following symmetry in the impulse
response:
h(n) = h(M ? 1 ? n) for M odd.
De?ve its frequency response and show that it has
linear phase.
(b) Discuss the Bilinear Transfonnation method of con-
verting analog IIR ?lter into digital 11R ?lter. What is
Frequency Warping? (7+8)
(6)
206/3'1'2/240/6000 ?