IMPORTANT QUESTIONS - EC6502 Principles of Digital Signal Processing-4

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 EC6502 Principles of Digital Signal Processing
Question Bank
UNIT IV
Part A

  1. What do you understand by a fixed point number? (Apr-2011)
  2. Express the fraction 7/8 and -7/8 in sign magnitude, 2’s complement and 1’s  complement.                         
  3. What are the quantization errors due to finite word length registers in digital filters?                                     
  4. What are the different quantization methods?                               
  5. What are the different types of fixed point number representation?
  6. What do you understand by sign-magnitude representation?
  7. What do you understand by 2’s complement representation?
  8. Write an account on floating point arithmetic?                                      
  9. What is meant by block floating point representation? What are its advantages?
  10. What are advantages of floating point arithmetic? (Nov-2011)
  11. Compare the fixed point and floating point arithmetic.                       
  12. What are the three quantization errors due to finite word length registers in digital filters?                                                                                       
  13. How the multiplication and addition are carried out in floating point arithmetic?
  14. Brief on co-efficient inaccuracy.
  15. What do you understand by input quantization error? (Nov-2013)
  16. What is product quantization error? (Nov-2010)
  17. What is meant by A/D conversion mode?
  18. What is the effect of quantization on pole locations?
  19.  What are the assumptions made concerning the statistical independence of  various noise sources that occur in realizing the filter?
  20. What is zero input limit cycle overflow oscillation    (Nov-2011)     
  21. What is meant by limit cycle oscillations? (Nov-2012,Apr-2011)
  22. Explain briefly the need for scaling digital filter implementation?
  23. Why rounding is preferred than truncation in realizing digital filter?
  24. Define the deadband of the filter?      (Nov-2014,May-2012)           
  25. Determine the dead band of the filter with pole at 0.5 and the number of bits used  for quantization is 4(including sign bit)
  26. Draw the quantization noise model for a first order IIR system
  27. What is meant by rounding? Draw the pdf of round off error
  28. What is meant by truncation? Draw the pdf of round off error (Nov-2010)
  29. What do you mean by quantization step size?
  30. What is scaling?(Nov-2014)
  31. State the methods used to prevent overflow.(Nov-2013)
  32. Find the quantization step size of the quantizer with 3 bits
  33. Give the expression for signal to quantization noise ratio and calculate the   improvement with an increase of 2 bits to the existing bit.
  34. Express the following binary numbers in decimal
(a) (100111.1110)2       (b) (101110.1111)2    (c) (10011.011)2




PART-B
  1. Draw the quantization noise model for a second order system and explain  and find its steady state output noise variance
  1. Consider the transfer function H(z)=H1(z)H2(z) where

       Find the output round off noise power. Assume a1=0.5 and a2=0.6 and find out the output round off noise power.                                                                                                   
  2. Find the effect of coefficient quantization on pole locations of the given second order IIR system when it is realized in direct form I and in cascade form. Assume a word length of 4-bits through truncation. 
      
  1. Explain the characteristics of Limit cycle oscillations with respect to the system described by the differential equations. y(n)=0.95y(n-1)+x(n) and determine the dead band of the filter.                               
  2. i) Describe the quantization errors that occur in rounding and truncation in 2’s complement.  
ii) Draw a sample/hold circuit and explain its operation.(Nov-2014,May-2014,Nov-2010,May-2011)
   
  1. Express the following decimal numbers in binary form
            (a) 525    (b) 152.1875 (c) 225.3275
  1. Express the decimal values 0.78125 and -0.1875 in (i) 1’s complement form (ii)sign magnitude form (iii) 2’s complement form.
  2. Express the decimal values  -6/8 and 9/8 in (i) Sign magnitude form (ii) 1’s complement form and (iii) 2’s complement form
  3. Study the limit cycle behavior of the following systems
(a)    y(n) = 0.7y(n-1) + x (n)
(b)   y(n) = 0.65y(n-2) + 0.52y (n-1) + x (n)
  1. Derive the quantization input noise power and determine the signal to noise ratio of the system.  (Nov-2014)
  2. Derive the truncation error and round off error noise power and compare both errors.
  3. Explain product quantization error and coefficient quantization error with examples (Nov-2014,April-2011,May-2014)
  4. Derive the scaling factor so that prevents the overflow limit cycle oscillations in a second order IIR system.
  5. The input to the system y(n)=0.999y(n-1)+x(n) is applied to an ADC. What is the power produced by the quantization noise at the output of the filter if the input is quantized to
(a) 8 bits      (b) 16 bits                                                                                   
  1. Convert the following decimal numbers into binary:                     
(a) (20.675)     (b) (120.75)
  1. Find the steady state variance of the noise in the output due to  quantization of input for the first order filter y(n)=ay(n-1) + x(n)   
  2. The output of an A/D  is fed through a digital system whose system function is
            H(z)=0.6z/z-0.6. Find the output noise power of the digital system=8 bits.
  1. a. Write a short note on limit cycle oscillation.      (Nov-2010,Nov-2011)                                                                                                    b. Explain in detail about signal scaling.  ((Nov-2011,May-2012)
  2. A digital system is characterized by the difference equation
y(n)=0.95y(n-1)+x(n). Determine the dead band of the system when x(n)=0  and y(-1)=13
  1. Two first order filters are connected in cascaded  whose system functions of the
individual sections are H1(z)=1/(1-0.8z-1)  and H2(z)=1/(1-0.9z-1 ). Determine the
overall output noise power.           
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