Visvesvaraya Technological University (VTU) 2006 B.E Electrical and Electronics Engineering 5th SEM / DIGITAL SIGNAL PROCESSING - Question Paper
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Fifth Semester B.E. Degree Examination, January/February 2006 Electrical & Electronics Engineering Digital Signal Processing
Time; 3 hrs.) [Max.Marks: 100
Note: 1. Answer any fIVE full questions.
2. Missing data may be suitably assumed but a mention of It Is a must.
3. Do no use Alter tables.
1. (a) Give fa(n) = u(n) - u(n - 6) determine x(w) and x(k) If x(w) Is sampled at wk = Xfor = 0,1,2,3. Determine an expression to reconstruct x(n) from x(k)
and also draw the reconstructed x(n). i'
4 -pt DFT x(l)
I) If G{k) = Wlkx{k) find g(n)
(10 Marks)
(b) Given x(n) = (i)n [u(n) - u(n - 4)] determine the following without computing
Ii) (A)a*(A)
71=0
:c(0) + x(2)
(10 Marks)
2. (a) A discrete time signal x(n) = {1,4,1,4,1} Is passed through a LSI system with
Impulse response h(n) = {A, } to generate y(n). Determine y(n) If DFT based convolution scheme is employed. (10 Marks)
<b) Derive and draw the complete declmatlon-ln-frequency flow chart to compute DFT of a 8-pt sequence. Mark all Inter mediate outputs. (10 Marks)
3. <a) Compute 8-pt real sequence given following DFT samples
-(&) {2,0.5 jl.207,0,0.5-7*0.207,0} using a FFt algorithm which accepts Input in a bit-reversed order. (10 Marks)
(b) Show that symmetry and antisymmetry In Impulse response of a FIR filter leads to linear phase characteristics. (10 Marks)
4. (a) A poie zero plot of a discrete time system is as shown In fig. 4a. Obtain transfer
function of the system and realize the same in cascade and parallel form. Use only 2nd order structures. (1 a Marks)
Contd.... 2
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(b) Check whether the following system has linear phase characteristics and further draw the linear phase realization of the same
H{Z) = 1 + + \%~2 + + jZ~4 + Z~5. (6 Marks)
5. (a) Use the technique of impulse Invariance to derive a low pass HR digital filter from
a second order Butter worth analog filter with 3-dB cutoff frequency of 3kHz, The sampling rate used is 30kHz. (10 Marks)
(b) Derive the mapping function used in transforming analog filter to digital filter by bilinear transformation. Show that this transformation preserves the frequency selectivity and stability properties of analog filter, (10 Marks)
6. (a) Determine the order and the poles of a type I low pass Chebyshev filter that has
a ldB ripple In the pass band and pass band frequency of flp = 10007T rad/sec, a stopband of 20007rra<2/,sec and an attenuation of 40dB or more. (10 Marks)
(b) Using bilinear transform, design a highpass filter, monotonic in pass band with cutoff frequency of 1000 Hz and down to lOdB at 350Hz, The sampling frequency is 5000 Hz, (10 Marks)
7. Design an ideal high pass filter with the following frequency response using i)' Rectangular window ii) Hanning window
The filter must have a length = 7. Compare the two designs for their magnitude response and comment on therm.
(Note : Hanning window W(n) = 0-5 -f 0.5 cos for -(N - l)/2 to
(~1) otherwise It is zero) (20 Marks)
8. Write an explanatory notes on :
a) DSP's In DTMF signal detection
b) Inplace computation & Bultinfly operation
c) DSP architecture
d) Effects of window characteristics on filter response. (4x5=20 Marks)
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