UNIT IV
PART – A
An analog filter has a transfer function H(s) = 1 / s+2. Using impulse invariance
method, obtain pole location for the corresponding digital filter with T = 0.1s.
What is frequency warping in bilinear transformation?
If the impulse response of the symmetric linear phase FIR filter of length 5 is
h (n) = {2,3,0,x,y}, find the values of x and y.
What is prewarping? Why is it needed?
Find the digital transfer function H (z) by using impulse invariance method for the analog transfer function H(s) = 1 / s+2.
What are the different structures of realization of FIR and IIR filters?
What are the methods used to transform analog to digital filters?
State the condition for linear phase in FIR filters for symmetric and anti symmetric response.
Draw a causal FIR filter structure for length M= 5.
What is bilinear transformation? What are its advantages?
Write the equation of Barlett (or) triangular and Hamming window.
Write the equation of Rectangular and Hanning window.
Write the equation of Blackman and Kaiser window.
Write the expression for location of poles of normalized Butter worth filter.
Pk = ± Ωc ej (N+2k +1) π / 2N
Where k = 0, 1, ……. (N-1) and for a normalized filter Ωc = 1 rad / sec
Write the expression for location of poles of normalized Chebyshev filter.
Draw the magnitude response of 3rd order Chebyshev filter.
Draw the magnitude response of 4th order Chebyshev filter.
Draw the basic FIR filter structure.
Draw the direct form – I structure of IIR filter.
Draw the direct form – II structure of IIR filter.
Draw the cascade form realization structure of IIR filter.
Draw the parallel form realization structure of IIR filter.
When cascade form realization structure is preferred in filters?
Distinguish between FIR and IIR filters.
Compare analog and digital filters.
Why FIR filters are always stable?
Because all its poles are located at the origin.
State the condition for a digital filter to be causal and stable.
What are the desirable characteristics of windows?
Give the magnitude function Butterworth filter. What is the effect of varying the order of N on magnitude and phase response?
List out the properties of Butterworth filter.
List out the properties of Chebyshev filter.
Give the Chebyshev filters transfer function and draw its magnitude response.
Give the equation for the order ‘N’ and cut off frequency Ωc of Butterworth filter
Why impulse invariance method is not preferred in the design of IIR filter other than low pass filters?
What are the advantages and disadvantages FIR filters?
What are the advantages and disadvantages IIR filters?
What is canonic structure?
If the number of delays in the structure is equal to the order of the difference equation or order of transfer function, then it is called canonic form of realization.
Compare Butterworth and Chebyshev filters.
What are the desirable and undesirable features of FIR filters?
What are the design techniques of designing FIR filters?
Fourier series method
Windowing technique
Frequency sampling method
PART –B
1. With suitable examples, describe the realization of linear phase FIR filters (8)
2. Convert the following analog transfer function H(s) = (s+0.2) / [(s+0.2)2 + 4] into
equivalent digital transfer function H (z) by using impulse invariance method assuming
T= 1 sec. (8)
3. Convert the following analog transfer function H(s) = 1 / (s+2) (s+4) into
equivalent digital transfer function H (z) by using bilinear transformation with T = 0.5
sec.
4. Convert the following analog transfer function H(s) = (s+0.1) / [(s+0.1)2 + 9] into
equivalent digital transfer function H (z) by using impulse invariance method assuming
T= 1 sec. (8)
5. Convert the following analog transfer function H(s) = 2/ (s+1) (s+3) into
equivalent digital transfer function H (z) by using bilinear transformation with T = 0.1
sec.Draw the diect form – II realization of digital filter. (8)
6. Design a high pass filter of length 7 samples with cut off frequency of 2 rad / sec
using Hamming window. Plot its magnitude and phase response. (16)
7. For the constraints
0.8 ≤ │H(ω)│≤ 1.0 , 0 ≤ ω ≤ 0.2π
│ H(ω)│ ≤ 0.2, 0.6 π ≤ ω ≤ π
With T= 1 sec determine the system function H(z) for a Butterworth filter using
bilinear transformation. (16)
8. Describe the effects of quantization in IIR filter. Consider a first order filter with
difference equation y (n) = x (n) + 0.5 y (n-1).Assume that the data register length is 3
bits plus a sign bit. The input x (n) = 0.875δ (n). Explain the limit cycle oscillations in
the above filter, if quantization is preferred by means of rounding and signed
magnitude representation is used. (16)
9. With a neat sketch explain the architecture of TMS 320 C54 processor. (16)
10. For the constraints
0.7 ≤ │H(ω)│≤ 1.0 , 0 ≤ ω ≤ π/2
│ H(ω)│ ≤ 0.2, 3π/4 ≤ ω ≤ π
With T= 1 sec, design a Butterworth filter. (16)
11. Explain the quantization effects in design of digital filters. (16)
12. Discuss about the window functions used in design of FIR filters (8)
13. Obtain the cascade and parallel realization of system described by difference equation
y(n) = -0.1 y(n-1) + 0.2 y(n-2) + 3x(n) +3.6 x(n-1) + 0.6 x(n-2) (10)
14. Design a digital Butterworth filter satisfying the following constraints with T= 1 sec,
using Bilinear transformation.
0.707 ≤ │H (ω) │≤ 1.0, 0 ≤ ω ≤ π/2
│ H (ω) │ ≤ 0.2, 3π/4 ≤ ω ≤ π (16)
15. Design a digital Chebyshev filter satisfying the following constraints with T= 1 sec,
using Bilinear transformation.
0.707 ≤ │H (ω) │≤ 1.0, 0 ≤ ω ≤ π/2
│ H (ω) │ ≤ 0.2, 3π/4 ≤ ω ≤ π (16)
18. Draw and explain cascade form structure for a 6th order FIR filter. (6)
19. Explain impulse invariance method of digital filter design. (10)
20. Derive an expression between s- domain and z- domain using bilinear transformation.
Explain frequency warping. (10)
21. Draw the structure for IIR filter in direct form – I and II for the following transfer
Function H (z) = (2 + 3 z-1) (4+ 2 z-1 +3 z-2) / (1+0.6 z-1) (1+ z-1+0.5 z-2) (10)
22. Design a filter with
Hd(ω) = e-j2ω - π/4 ≤ ω ≤ π/4
= 0 π/4 ≤ ω ≤ π
Using a Hamming window with N= 7 (16)
23. Discuss about frequency transformations in detail. (8)
24. Design a LPF with
Hd(ω) = e-j3ω - 3π/4 ≤ ω ≤3π/4
= 0 3π/4 ≤ ω ≤ π
Using a Hamming window with N= 7 (16)
25. Using the bilinear transformation and a low pass analog Butterworth prototype,
design a low pass digital filter operating at a rate of 20 KHz and having pass band
extending to a 4 KHz with a maximum pass band attenuation of 0.5 dB and stop band
starting at 5KHzwith a minimum stop band attenuation of 10 dB. (16)
26. Using the bilinear transformation and a low pass analog Chebyshev type I prototype,
design a low pass digital filter operating at a rate of 20 KHz and having pass band
extending to a 4 KHz with a maximum pass band attenuation of 0.5 dB and stop band
starting at 5KHzwith a minimum stop band attenuation of 10 dB. (16)
27. Obtain the cascade realization of linear phase FIR filter having system function
H(z) = ( 1+1/2 z-1 + z-2) (2 + ¼ z-1 +2z-2) using minimum number of multipliers.(8)
28. Design an ideal Hilbert transformer having frequency response
H(ejω) = j for -π ≤ ω ≤ 0
= -j for 0≤ ω ≤ π
for N=11, using i. rectangular window
ii. Blackmann window
29. Obtain the direct form – I, direct form – II, cascade and parallel form of realization
for the system y(n) = -0.1 y9n-1) + 0.2 y(n-2) + 3 x(n) + 3.6 x (n-1) + 0.6 x(n-2)
30. Using Bilinear transformation and a low pass analog Butterworth prototype, design a
low pass digital filter operating at the rate of 20k Hz and having pass band extending
to 4 kHz with maximum pass band attenuation of 10 dB and stop band starting at 5
kHz with a minimum stop band attenuation of 0.5 dB
31. Using Bilinear transformation and a low pass analog Chebyshev type I prototype,
design a low pass digital filter operating at the rate of 20k Hz and having pass band
extending to 4 kHz with maximum pass band attenuation of 10 dB and stop band
starting at 5 kHz with a minimum stop band attenuation of 0.5 dB
32. Design a low pass filter using Hamming window for N=7 for the desired frequency
Response D (ω) = ej3ω for -3π / 4 ≤ ω ≤3π / 4
= 0 for 3π / 4 ≤ ω ≤ π
33. Design an ideal differentiator for N=9 using Hanning and triangular window
UNIT – V
PART - A
1. Compare fixed point arithmetic and floating point arithmetic.
2. What is product quantization error or product round off error in DSP?
3. What are the quantization methods?
4. What is truncation and what is the error that arises due to truncation in floating
point numbers?
What is meant by rounding? Discuss its effects?
What are the two kinds of limit cycle oscillations in DSP?
Why is rounding preferred to truncation in realizing digital filters?
What are the 3 quantization errors due to finite word length registers in digital filters?
List out the features of TMS 320 C54 processors.
What are the various interrupt types supported by TMS 320 C54?
Mention the function of program controller of DSP processor TMS 320 C54.
List the elements in program controller of TMS 320C54.
What do you mean by limit cycle oscillations?
What is pipelining? What is the pipeline depth of TMS 320 C54 processor?
What are the different buses of TMS 320 C54 processor?
What are quantization errors due to finite word length registers in digital filters?
Differentiate between Von Neumann and Harvard architecture.
Define limit cycle oscillations in recursive systems.
How to prevent overflow in digital filters?
PART –B
1. Describe the function of on chip peripherals of TMS 320 C54 processor. (12)
2. What are the different buses of TMS 320 C54 processor? Give their functions. (4)
3. Explain the function of auxiliary registers in the indirect addressing mode to point the
data memory location. (8)
4. Explain about the MAC unit. (8)
5. What is meant by instruction pipelining? Explain with an example how pipelining
increases through put efficiency. (8)
6. Explain the operation of TDM serial ports in P-DSPs (8)
7. Explain the characteristics of a limit cycle oscillation with respect to the system
described by the equation y (n) = 0.95 y (n-1) + x (n).Determine the dead band of the
filter. (10)
8. Draw the product quantization noise model of second order IIR filter. (6)
9. In a cascaded realization of the first order digital filter, the system function of the
individual section are H19z) = 1 / (1-0.9 z-1) and H2(z) = 1 / (1-0.8z-1). Draw the
product quantization noise model of the system and determine the output noise
power. (16)
10. Explain the statistical characterization of quantization effects in fixed point
realization of digital filter. (16)
11. Give a detailed note on Direct memory Access controller in TMS 320 C54x
processor.
12. Find the effect of quantization on the pole locations of the second order IIR filter
Given by H(z) = 1 / (1-0.5z-1) (1- 0.45 z-1) when it is realized in direct form – I and in
cascade form. Assume a word length of 3 bits.
13. Determine the variance of the round off noise at the output of the two cascade
realizations of the filters with system functions H1 (z) = 1 / 1-0.5 z-1
H2 (z) = 1 / 1- 0.25 z-1
Cascade I, H (z) = H1 (Z) H2 (z)
Cascade II, H (z) = H2 (z) H1 (z)
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