STUPIDSID
1 (a)
Assume that a complex multiplier takes 1 micro sec to perform one multiplication and that the amount of time to compute a DFT is determined by the amount of time to perform all the multiplications.
(i) How much time does it take to compute a 1024 point DFT directly?
(ii) How much time is required is FFT is used?
(i) How much time does it take to compute a 1024 point DFT directly?
(ii) How much time is required is FFT is used?
5 M
1 (b)
Let h[n] be the unit impulse response of a Low Pass filter with a cutoff frequency ωc, what type of filter has a unit sample response g[n]= (-1)n h[n].
5 M
1 (c)
A two pole low pass filter has the system function \[H\left(z\right)=\frac{b_0}{{\left(1-pz^{-1}\right)}^z}\] Determine the values of b0 and P
5 M
1 (d)
Consider filter with transfer function. Identify the type of filter and justify it.
\[ H\left(z\right)=\frac{z^{-1}-a}{1-az^{-1}}\]
\[ H\left(z\right)=\frac{z^{-1}-a}{1-az^{-1}}\]
5 M
2 (a)
The unit sample response of a system is h(n)={3,2,1} use overlap-add method of linear filtering to determine output sequence for the repeating input sequence x[n]= {2,0,-2,0,2,1,0,-2,-1,0}
10 M
2 (b)
For a given sequence x(n)= {2,0,0,1}, perform following operation :
(i) Find out the 4 point DFT of x(n)
(ii) Plot x(n), its periodic extension xp(n) and xp(n-3)
(iii) Find out 4 point DFT of xp(n-3)
(iv) Add phase angel in (i) with factor - \[-\ \ [\frac{2\pi{}rk}{N}]\] where N=4, r=3, k=0,1,2,3
(v) Comment on the result you had in point (i) and (ii)
(i) Find out the 4 point DFT of x(n)
(ii) Plot x(n), its periodic extension xp(n) and xp(n-3)
(iii) Find out 4 point DFT of xp(n-3)
(iv) Add phase angel in (i) with factor - \[-\ \ [\frac{2\pi{}rk}{N}]\] where N=4, r=3, k=0,1,2,3
(v) Comment on the result you had in point (i) and (ii)
10 M
3 (a)
The transfer function of discrete time causal system is given below :
\[H\left(z\right)=\frac{1-z^{-1}}{1-0.2z^{-1}-0.15z^{-2}}\]
(i) Find the difference equation
(ii) Draw cascade and parallel realization
(iii) Show pole-zero diagram and then find magnitude at ω = 0 and ω= π
(iv) Calculate the impulse response of the system.
\[H\left(z\right)=\frac{1-z^{-1}}{1-0.2z^{-1}-0.15z^{-2}}\]
(i) Find the difference equation
(ii) Draw cascade and parallel realization
(iii) Show pole-zero diagram and then find magnitude at ω = 0 and ω= π
(iv) Calculate the impulse response of the system.
10 M
3 (b)
Obtain the lattice realization for the system :
\[H\left(z\right)=\frac{1+3z^{-1}+3z^{-2}+z^{-3}}{1+\frac{3}{4}z^{-1}+\frac{1}{2}z^{-2}+\frac{1}{4}z^{-3}}\]
\[H\left(z\right)=\frac{1+3z^{-1}+3z^{-2}+z^{-3}}{1+\frac{3}{4}z^{-1}+\frac{1}{2}z^{-2}+\frac{1}{4}z^{-3}}\]
10 M
4 (a)
What is a linear phase filter? What conditions are to be satisfied by the impulse response of an FIR system in order to have a linear phase? Plot and justify compulsory zero locations for symmetric even antisymmetric even and antisymmetric odd FIR filters.
10 M
4 (b)
Determine the zero of be following FIR system and indicate whether the system is minimum phase, maximum phase, or mixed phase
\[H_1\left(z\right)=6+z^{-1}-z^{-2}\]
\[H_2\left(z\right)=1-z^{-1}-6z^{-2}\]
\[H_1\left(z\right)=1-\frac{5}{2}z^{-1}-\frac{3}{2}z^{-2}\]
\[H_1\left(z\right)=1+\frac{5}{3}z^{-1}-\frac{2}{3}z^{-2}\]
Comment on the stability of the minimum and maximum phase system
\[H_1\left(z\right)=6+z^{-1}-z^{-2}\]
\[H_2\left(z\right)=1-z^{-1}-6z^{-2}\]
\[H_1\left(z\right)=1-\frac{5}{2}z^{-1}-\frac{3}{2}z^{-2}\]
\[H_1\left(z\right)=1+\frac{5}{3}z^{-1}-\frac{2}{3}z^{-2}\]
Comment on the stability of the minimum and maximum phase system
10 M
5 (a)
A digital low pass filter is required to meet the following specification:
Pass band ripple : ≤1dB
Pass band edge : 4KHz
Stop band attenuation : ≥ 40dB
Stop band edge : 8KHz
Sampling rate : 24KHz
Find order, cutoff frequency and pole locations for Butterworth filter using bilinear transformation.
Pass band ripple : ≤1dB
Pass band edge : 4KHz
Stop band attenuation : ≥ 40dB
Stop band edge : 8KHz
Sampling rate : 24KHz
Find order, cutoff frequency and pole locations for Butterworth filter using bilinear transformation.
10 M
5 (b)
Design an FIR digital filter to approximate an ideal low pass filter with passband gain of unity, cut-off frequency of 950Hz and working at a sampling frequency of Fs=5000 Hz. The length of the impulse response should be 5. Use a rectangular window.
10 M
6 (a)
Explain the need of a low pass filter with a decimator and mathematically prove that ωy = ωxD.
10 M
6 (b)
Why is the direct form FIR structure for a multirate system inefficient? Explain with neat diagrams how this inefficiency is overdone in implementing a decimator and an interpolator.
10 M
Write short notes (any four ) :
7 (a)
DTMF detection using Geortzel algorithm
5 M
7 (b)
Filter bank
5 M
7 (c)
Comparison of FIR and IIR filters
5 M
7 (d)
Split radix FFT
5 M
7 (e)
Optimum Equiripple Linear phase FIR filter design
5 M
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