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**PYQ**Institute:
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Biju Patnaik University of Technology BPUT
**Course:
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B.Tech
**Specialization:
**Electrical Engineering**Views:
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**3 months ago**

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Total Number of Pages: 02
B.Tech
PEE6J005
6th Semester Regular Examination 2017-18
Advanced Digital Signal Processing
BRANCH: Electrical
Time: 3 Hours
Max Marks: 100
Q.CODE: C434
Answer Part-A which is compulsory and any four from Part-B.
The figures in the right hand margin indicate marks.
Q1
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
Q2
a)
b)
c)
d)
e)
f)
g)
h)
i)
j)
Part – A (Answer all the questions)
Answer the following questions: multiple type or dash fill up type
Down-sampling is a _________ process. (time-variant/ time-invariant)
Multistage implementation of sampling rate conversion ______ the
efficiency of the conversion.
The noise whitening filter for generating the innovation process for an
autoregressive process input is _______ filter (all-pole /all-zero).
Welch method is ____method of power spectrum estimation.
Levinson-Durbin algorithm is for solving _________.
The power density spectrum estimate is better is its variance is _____.
A delay of k samples is equivalent to a phase shift of ____.
______ is the maximum frequency that can be uniquely represented at a
sampling rate Fs=40 Hz.
Convolution of ( ) with ( ) smoothens spectrum of ( ), provided the
spectrum of ( ) is _____ compared to ( ).
An adaptive linear combiner with 3-weights has a error surface plot
of____ dimensions.
Answer the following questions: Short answer type
Define Wide-sense stationary process.
Give the block-diagram representation for down-sampling by a factor D.
Mention the frequency response of the filter used.
What is a noise whitening filter ?
Give the difference equation for an AR process.
What is leakage in the context of energy density spectrum estimate?
Give the weight updation rule for LMS algorithm, explaining each of the
terms in the expression.
What is meant by Wold representation of a stationary random process?
Explain the terms convergence and stability in reference to an
optimisation algorithm.
Cite two disadvantages of Least Mean Square algorithm.
Justify the words “adaptive” and “linear” in Adaptive Linear Combiner.
(2 x 10)
(2 x 10)

Part – B (Answer any four questions)
Q3 a) Given a signal ( ) ↔ ( ) , such that ( ) = 0 for | | > . The signal is
decimated by a factor D=2 to get ( ). Sketch ( ) and ( ) , and
justify whether ( ) can be reconstructed from the signal ( ) or not.
b) What do you understand by integer-band-positioned discrete time
signals? Explain with spectral diagrams, the effect of down-sampling on
an even-band-positioned bandpass signal.
(10)
(5)
Q4 a) Explain sub-band coding of speech signal with proper block diagram.
b) What do you mean by uniform analysis filer bank? Give the expressions
for impulse response, frequency response and system function of such a
filter. Draw the frequency response of a 4-component analysis filer bank.
(10)
(5)
Q5 a) Derive the time-domain expression for the output of Forward Linear
Prediction Error filter and draw the direct form-1 structure for the filter.
Explain what Normal Equations are in reference to this error function
expression.
b) What is the relationship between Forward Linear Prediction Error Filter
system function ( ) and Backward Linear Prediction Error Filter system
function ( ) . Determine the reflection coefficients { } of the lattice
filter corresponding to the FIR filter described by the system function :
1
H (z) A 2 (z) 1 2 z 1 z 2
3
(10)
Q6 a) Discuss Welch method for power spectrum estimation as an modified
form of Bartlett method.
b) Prove that periodogram is not a consistent estimate of the true power
density spectrum.
(10)
Q7 a) Differentiate between direct method and indirect method of energy density
spectrum estimation. Explain the leakage problem encountered in the
computation of energy density spectrum from a finite-duration signal.
b) Explain the Bartlett method of power spectrum estimation with supporting
mathematical expressions.
(10)
Q8 a) What do you understand by noise cancellation? Explain adaptive noise
cancellation with block diagram and supporting mathematical
expressions.
b) Define mean square error for an adaptive linear combiner. Hence derive
the Wiener- Hopf equation for optimum filter coefficients for the same.
(10)
Q9 a) Derive the relationship between the autocorrelation function
( ) and
the filter parameters, if the power spectral density of the stationary
random process ( ) is a rational function, and the filter generates the
random process by filtering the white noise sequence ( ).
b) Explain rational power spectra for a stationary random process. Also
explain the three specific cases of rational power spectra? Write the
difference equation for each of them.
(10)
(5)
(5)
(5)
(5)
(5)

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