STUPIDSID
1 (a)
Compare impulse invariant and Bilinear transformation techniques.
5 M
1 (b)
A two pole low pass filter has the system function \[ H(z) = \dfrac {b_0}{(1-pz^{-1})^2) \] Determine the value of b0 and p such that the frequency response H(ω) satisfies the conditions \[ H(0)=1 \ and \ \bigg \vert H \left ( \dfrac {\pi }{4} \right ) \bigg \vert^2 = \dfrac {1}{2} \]
5 M
1 (c)
Explain Multi rate sampling? What are the basic methods? List the advantages of it.
5 M
1 (d)
Explain the sub band coding of speech signal as an application of multi rate signal processing.
5 M
2 (a)
If the impulse response of a FIR filters has the property h(n)=±;h(N-1-n), find the expression for magnitude response and phase and show that filters will have linear phase response.
10 M
2 (b)
An 8 point sequence x(n)={1,2,3,4,5,6,7,8}
i) Find X[k] using DIF-FFT algorithm
ii) Let x1[n]={5,6,7,81,2,3,4} using appropriate DFT property and result of part (i) determine X1[k].
i) Find X[k] using DIF-FFT algorithm
ii) Let x1[n]={5,6,7,81,2,3,4} using appropriate DFT property and result of part (i) determine X1[k].
10 M
3 (a)
Draw a lattice filter implementation for the all pole filter, \[ H(z) = \dfrac {1}{1-0.2z^{-1} + 0.4z^{-2}+ 0.6z^{-3}} \] and determine the number of multiplications, additions and delays required to implement the filter.
10 M
3 (b)
Compare minimum phase, maximum phase and mixed system. Determine the zeros of the following FIR systems and indicate whether the system is minimum phase, maximum phase or mixed phase, H(z)=6+z-1=z-2.
10 M
4 (a)
Develop DIT-FFT algorithm for decomposing the DFT for N=6 and draw the flow diagrams for (i) N=2×3 (ii) N=3×2
10 M
4 (b)
i) Convert the following analog filter system function into digital IIR filter by means of Bilinear transformation. The digital filter should have resonant frequency of ωt=Π/4 \[ Ha(S)= \dfrac {(s+0.1)}{[(s+0.1)^2 + 9]}
ii) For the analog transfer function \[ H(s) = \dfrac {1} {(s+1)(s+2)} \] Determine H(z) using impulse invariant technique. Assume T=1sec.
ii) For the analog transfer function \[ H(s) = \dfrac {1} {(s+1)(s+2)} \] Determine H(z) using impulse invariant technique. Assume T=1sec.
10 M
5 (a)
The transfer function discrete time causal system is given below. \[ H(z) = \dfrac {(1-z^{-1})}{(1-0.2 z^{-1}+0.15z^{-2})} \] i) Find the difference equation.
ii) DF-I and DF-II
iii) Draw Parallel and Cascade realization
iv) Show pole and zero diagram and find magnitude at ω=0 and ω=Π
ii) DF-I and DF-II
iii) Draw Parallel and Cascade realization
iv) Show pole and zero diagram and find magnitude at ω=0 and ω=Π
10 M
5 (b)
A filter is to be designed with the following desired frequency response \[ \begin {align*}
H(e^{i\omega})&=0 &; -\pi/4|\omega | \le \pi /4 \ \\
&= e^{-j2\omega} &; -\pi/4 \le |\omega | \le \pi \end{align*} \] Determine the filter coefficient h(n) if the window function is defined as \[ \begin {align*}
w(n) &=1, &0\le n \le 4 \\
&=0, &otherwise
\end{align*} \] Also determine the frequency response H(eiω) of the designed filter.
10 M
6 (a)
Determine H(z) for a digital Butterworth filter that satisfying the following constraints \[\begin {align*}
\sqrt{0.5} \le & \big \vert H_d (e^{j\omega}) \big \vert \le 1 &; 0 \le \omega \le \pi /2 \ \ \\
&\bigg \vert H_d (e^{j \omega}) \bigg \vert \le 0.2 &; 3 \pi/4 \le \omega \le \pi
\end{align*} \] With T=1 sec. Apply impulse invariant transformation.
10 M
6 (b)
i) A sequence is given as x(n)={1+2j, 1+3j, 2+4j, 2+2j}, from the basic definition, find X(k). If x1(n)={1,1,2,2} and x1 and x1(n)={1,1,2,2}. Find X1(k) and X2(k) by using DFT only.
ii) Sequence xp(n) is a periodic repletion of sequence x(n). What is the relationship between Ck of discrete time Fourier series of xp(n) and X(k) of x(n)?
ii) Sequence xp(n) is a periodic repletion of sequence x(n). What is the relationship between Ck of discrete time Fourier series of xp(n) and X(k) of x(n)?
10 M
Write short note on (any three):
7 (a)
Adaptive television echo cancellation
7 M
7 (b)
Goertzel algorithm
7 M
7 (c)
Decimation by integer factor (M) and interpolation by integer factor (L).
7 M
7 (d)
Overlap add and overlap save method for long data sequence.
7 M
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