Biju Patnaik University of Technology 2008-6th Sem B.Tech (B Tech),ester digital signal processing . - Question Paper
BPUT(B Tech),6th semester digital signal processing ques. paper.
Sixth Semester Examination - 2008 DIGITAL SIGNAL PROCESSING
Full Marks-70 Time: 3 Hours
Answer either from Set-A orSet-B, but not from both.
(WL
Answer Question No. 1 which is compulsory and any five from the rest.
The figures in the right-hand margin indicate marks.
1. Answer the following questions r 2x10
(a) Find the response of the system if a = 1, b _ -lt x(n) = fi(n) and the system is initially at rest.
(b) Find oul the Nyquist rate for the signal x{t) = 25 COS (500 nl).
X(rt)
y(n)
(c) What is the stability condition of an LTf system ?
(d) At which band an ideal filter is distortionless ?
(e) How the DFT and DTFT of one discrete 3* time signal related ?
(f) Find oul the impulse response of the LTI system given by 11A11 y(n) = k,x(n) + k2x{n-1) + k3x{n-2). I VVL
(g) What are the advantages of FFT over DFT?
(hj Draw the signal flow graph ot a first order 4 digital filter,
(i) Show whether the systems are (i) Linear / Non linear, (ii) TV/TIV.
y(n) = x(k)
(j) What is the aliasing effect ?
(a) Determine the impulse response for the given system described by difference
equation.
6
y{n}-4y(n-1) + 4y {n-2) = x(n)-x{n-l) (b) Compute and sketch the step response of
the system.
4
(a) Determine convolution of the following pairs
of signal by means of ZT.
6
x(n) = 0.5n u(n)f x2(n) = COS /in u(n).
(b) Consider the Fir filter represented as y(n) = x(n) +x{n-4). Compute and sketch the magnitude and phase spectrum. 4
(a) Let x(n) be a real valued N point sequence* Develop a method to compute a N point OFT xk), which contains only the odd harmonics by using a real N/2 point DFT. 5
(b) Perform linear convolution of the following sequence by over/ap add melhod. 5 x(n) = {1. -1, 2, -2, 3, -3, 4, 4)
5. x(n) = 5fn)+28(n-2) + 5<n-3) *
(i) Find the four point DFT of x(n), 5
(If) if y(n) is the four point circular convolution of x(n) with itself, find y{n) and four point DFT Y{k). 5
a Design an FIR digital filter approximating the ideal tow frequency response.
i i n 1, y<-
' ' 6 6 f 1
(i) Determine the coefficients of 25 tap filter based on window method with a rectangular window. 5
(ii) Plot the magnitude and phase response of the filter. 5
7. (a) With impulse invariance, a first order pole in Ha(s) at s = sk is mapped to a pole in H(Z) atZ = e4Ti
1 1
--=$ <----
S-Sk 1-esNTz-1
Determine how a second order pole is mapped with impulse invariance. 6
(b) A second order continuous time filter has a system function
t 1 H(s) = +
s-a a-b
Where a <0 and b<0 are real. Determine the locations of poles of H<Z> if the filter designed using impulse invariance technique with T = 2 sec. 4
8. (a) Find the direct form II realization for the system described by difference equation.
6
Y(n) = y(n-1}-y(n-2) + x(n,)~x(x-1j
(b) Explain the power spectrum estimation using Lhe Bartlet method. 4
SET - B
Answer Question No. 1 which is compulsory and any five from the rest
The figures in thB right-hand margin
1. Answer the following question : 2x10
(a) Find the response ot the system if a = 1, b = -1, x(n) = 5{n) and Ihe systepi is
initially at rest X<n)
(b) Find out the Nyquist rale for the signal x(l) = 25 COS (500 tel).
(c) What is the stability condition of an LTI system ?
3.
(d) At which band an ideal filter is distortionless ?
(e) How the DFT and DTFT of one discrete time signal related ?
(f) Find out the impulse response of the LTI system given by | yy |_ y{n) = kn) + k2x(n-1) + kgx(n-2).
(g) What are the advantages of FFT over 1 DFT ?
(h) Draw the signal flow graph of a first order digital filter.
4.
(i) Show whether the systems are (i) Linear / Non linear, (ii) TVjTIV.
y<n) - x(n2).
(j) What is the aliasing effect ? CPEC 5302 6
(a) Determine the impulse response for the given system described by difference equation, 6
y (n)-4y(n -1) + 4y (n-2) - x (n)-x{n-1)
(bj Compute and sketch the step response of the system, 4
y(n) = A S x(n-k).
M k%o
(a) Find the direct form II realization for the system described by difference equation.
6
Y(n) = |y(n-1)=|y(n-2) + x(n) ~ x(x -1)
(b) Consider the Fir filter represented as y(n)=x(n) + x(n-4). Compute and sketch the magnitude and phase spectrum. 4
(a) Let x(n) be a real valued N point sequence, Develop a method to compute a N point DFT x*(k), which contains only the odd harmonics by using a real N/2 point DFT 5
(b) Perform linear convolution of the following sequence by overlap add method. 5
x(n) = {1, -1 r 2, -2, 3, -3, 4, -4} h(n) = {-1, 1}.
xfn)(n)+26(n-2)+ S(n-3)
(i) Find I he four point DFT of x(n)* 5
(ii) lfy(n) is the four point cfrcufar convolution of x(n) with itself, find y(n) and four point DFTY(k). 5
Determine the mean and the autocorrelation of the sequence x(n), which is the output of a ARMA
0,1) process described by difference equation x(n) = 0.5 x(n-1)+w(n)-w(n-1). 10
For zero mean, jointly Gaussian random variable X1, X2, X3, X4 it is known that E(XI X2 X3 X4) = E(X1 X2) E(X3 X4) + E (XI X3} E(X2 X4J + E(X1 X4) E{X2 X3) I W| use this result to derive the mean square value of r'*K< m) and the variance which is Var [r(m)j E [|rtt (m)f2] - E \[r'n (m)]|2 10 Determine the coefficient {h(n)} of a linear phase FIR of length N = 15 which has a symmetric unit sample response and a frequency response that
7,
j
a.
p- k = 0,1,2, 3i , 15 J [0, k-4, 5,6, 7 satisfies the condition. ] q
r.1 X*
8
V
-C
CPEC 5302
|
Attachment: |
| Earning: Approval pending. |
