DEPARTMENT OF EI DIGITAL SIGNAL PROCESSING...
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This PDF is Created by Simpo PDF Creator unregistered version - http://www.simpopdf.com “Study hard, for the well is deep, and our brains are shallow.” DEPARTMENT OF EI DIGITAL SIGNAL PROCESSING ASSIGNMENT 1 Q.1. What are the advantages of representing a digital filter in the block diagram form. Q.2. Determine the cascade and parallel realizations for the system described by the system function: = − − + − − − + − − Q.3. Obtain the direct form I and II structures for a third order IIR transfer function which is given as: = . + . + . . + . + . − . Q.4. What are canonic and non-canonic structures? Q.5. Explain parallel form realization. Q.6. Draw the direct-form I realization structure of 3 rd order system . Q.7. Explain advantage of direct form structures. Q.8. What is ladder structure? Q.9. Explain continued fraction expansion method? Explain with an example.
Transcript of DEPARTMENT OF EI DIGITAL SIGNAL PROCESSING...
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“Study hard, for the well is deep, and our brains are shallow.”
DEPARTMENT OF EI
DIGITAL SIGNAL PROCESSING ASSIGNMENT 1
Q.1. What are the advantages of representing a digital filter in the block diagram form. Q.2. Determine the cascade and parallel realizations for the system described by the system function:
=� � − − +
− − − + − −
Q.3. Obtain the direct form I and II structures for a third order IIR transfer function which is given as:
=. � � + . � � � � + . � �
. + . + . � � � − .
Q.4. What are canonic and non-canonic structures? Q.5. Explain parallel form realization. Q.6. Draw the direct-form I realization structure of 3rd order system . Q.7. Explain advantage of direct form structures. Q.8. What is ladder structure? Q.9. Explain continued fraction expansion method? Explain with an example.
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ASSIGNMENT 2
Q.1. Explain the mapping from s-plane to z-plane .
Q.2. Explain the magnitude characteristics of the physically realizable filter.
Q.3. Use impulse invariance method to design a digital filter from an analog prototype that have a system function :
=+
( + ) +
Q.4. Describe the complete mapping with the expressions and diagrams from s-plane to z-plane if bilinear transformation is used. What do you mean by ‘frequency warping effect’ and ‘pre-warping’ with respect to bilinear transformation.
Q.5. Make use of bilinear transformation to obtain H(z) if it is given that :
Ha(s) = ( )
and T = 0.1s
Q.6. Design a digital Butterworth filter using impulse invariant method if:
0.707≤|H (ejωωωω) |≤1 , 0≤|ωωωω|≤0.5π
|H (ejωωωω) |≤0.2 , π≤|ωωωω|≤π
Q.7. Write short note:
a) Butterworth filter
b) Chebyshev filter
Q.8. Describe the complete mapping with the expressions and diagrams from s-plane to z-plane if impulse invariant transformation is used.
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ASSIGNMENT 3
Q.1. Explain symmetric and anti-symmetric FIR filters.
Q.2. What is meant by linear phase response? Prove that filter with the following response has linear phase response: h(n) = [2 1 1 2] .
Q.3. Show that if z1 is the zero of the linear phase FIR filter, then 1/ z1 is also zero of the filter.
Q.4. Design an FIR filter to meet the following specifications:
Pass band edge frequency=2 KHz
Stop band edge frequency=5 KHz
Stop band attenuation=50dB
Sampling frequency=Fs=20 KHz
Use Hamming Window.
Q.5. Design an FIR linear phase filter using Kaiser window to meet the following specifications:
0.99≤|H (ejωωωω) |≤1.01 , 0≤|ωωωω|≤0.19π
|H (ejωωωω) |≤0.01 , 0.21π≤|ωωωω|≤π
Q.6. Compare the frequency – domain characteristics of the different types of window.
Q.7. Design a bandpass filter which approximates the ideal filter with cut-off frequencies at 0.2 rad/sec and 0.3 rad/sec. The filter order is M=7. Use the Hanning window function.
Q.8. Explain Gibb`s phenomenon.
Q.9. Explain Window function.
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ASSIGNMENT 4 Q.1. What are the advantages of DSP over ASP? Q.2. State and prove the symmetry property of DFT. Q.3. Obtain DFT of unit impulse function δδδδ(t). Q.4. compute the DFT of following window function :
w(n) = u(n) – u(n-N) Q.5. Determine DFT of four point sequence x(n) = [1 2 3 4] . Q.6. Explain the relation of DFT to Z-transform . Q.7. State and prove Duality property of DFT. Q.8. Compute circular convolution of : x(n) = [0 1 2 3] and h(n) = [1 5 3 5] . Q.9. Compute linear convolution using circular convolution of sequences x (n) = [1 2 3] and h(n) = [1 2]. Q.10. DFT of a sequence x(n) is given by X(k) = [4 1+2j j 1-3j]. Using DFT property only determine x*(n).
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ASSIGNMENT 5
Q.1. Derive DIT FFT flowgraph for N=4.
Q.2. Derive DIF FFT flowgraph for N=16.
Q.3. Compare the number of multiplications and additions which are needed for direct computation of DFT with those needed for radix-2 FFT algorithms.
Q.4. Determine how a 2N-point DFT of a real valued sequence may be computed using an N-point FFT algorithm.
Q.5. Determine the four point DFT of the sequence x(n)={1 0 2 1} using DIT FFT algorithm.
Q.6. Explain In-Place computation for DFT.
Q.7.Discuss the FFT algorithms for composite value of N.
Q.8. Derive the DIT IDFT FFT flowgraph for N=4.
Q.9. Determine eight point DFT of the sequence x(n)=[1 2 3 4] using DIT FFT.
Q.10. Determine IDFT of X(k)=[10,-2+2j,-2,-2-2j] using DIT FFT.
