Part – B (Answer any four questions)
Q3 a) In the context of decimation by a factor D, explain what the scope of its
efficient implementation. Obtain the efficient implementation of
decimation, when D=3, using polyphase structure and noble identities
with required block-diagram representation.
b) Plot the signals and their corresponding spectra for rational sampling
rate conversion by = and = . Assume the spectrum of the input
signal ( ) occupies the entire range − ≤ ≤ .
Q4 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
b) Consider the ARMA process generated by the difference equation:
x(n) 1.6 x(n 1) 0.63x(n 2) w(n) 0.9 w(n 1)
Determine the system function of the whitening filter and power spectral
density of the signal ( ).
Q5 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.
Q6 a) Differentiate between parametric and non-parametric methods for power
spectrum estimation, explaining one method of each class.
b) Prove that periodogram is not a consistent estimate of the true power
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
b) Explain the Bartlett method of power spectrum estimation with supporting
Q8 a) Prove that the error signal is uncorrelated (orthogonal to) with the input
signal in a linear adaptive filter, when the mean square error is minimum
i.e. the filter is optimum.
b) Explain Least Mean Square algorithm in reference to its special estimate
of gradient. Use it to derive the weight updation rule for LMS.
Q9 a) What do you understand by channel equalization? Explain adaptive
channel equalization with block diagram.
b) Define mean square error for an adaptive linear combiner. Hence derive
the Wiener-Hopf equation for optimum filter coefficients for the same.