EE6403                     DISCRETE TIME SYSTEMS AND SIGNAL PROCESSING            L T P C 3 0 0 3

OBJECTIVES:

· To classify signals and systems & their mathematical representation.

· To analyse the discrete time systems.

· To study various transformation techniques & their computation.

· To study about filters and their design for digital implementation.

· To study about a programmable digital signal processor & quantization effects.

UNIT I INTRODUCTION                                                                                  9

Classification of systems: Continuous, discrete, linear, causal, stable, dynamic, recursive, time variance; classification of signals: continuous and discrete, energy andpower; mathematical representation of signals; spectral density; sampling techniques, quantization, quantization error, Nyquist rate, aliasing effect.

UNIT II DISCRETE TIME SYSTEM ANALYSIS                                             9

Z-transform and its properties, inverse z-transforms; difference equation – Solution by ztransform,application to discrete systems - Stability analysis, frequency response – Convolution – Discrete TimeFourier transform , magnitude and phase representation.

UNIT III DISCRETE FOURIER TRANSFORM & COMPUTATION         9

Discrete Fourier Transform- properties, magnitude and phase representation - Computation of DFT using FFT algorithm – DIT &DIF using radix 2 FFT – Butterfly structure.

UNIT IV DESIGN OF DIGITAL FILTERS                                                       9

 FIR & IIR filter realization – Parallel & cascade forms. FIR design: Windowing Techniques – Need and choice of windows – Linear phase characteristics. Analog filter design – Butterworth and Chebyshev approximations; IIR Filters, digital design using impulse invariant and bilinear transformation - mWarping, pre warping.

UNIT V DIGITAL SIGNAL PROCESSORS                                                    9

Introduction – Architecture – Features – Addressing Formats – Functional modes - Introduction to Commercial DSProcessors.

TOTAL : 45 PERIODS 50

OUTCOMES:

·Ability to understand and apply basic science, circuit theory, Electro-magnetic field theory control theory and apply them to electrical engineering problems.

TEXT BOOKS:

1. J.G. Proakis and D.G. Manolakis, ‘Digital Signal Processing Principles, Algorithms and Applications’, Pearson Education, New Delhi, PHI. 2003.

2. S.K. Mitra, ‘Digital Signal Processing – A Computer Based Approach’, McGraw Hill Edu, 2013.

 3. Robert Schilling & Sandra L.Harris, Introduction to Digital Signal Processing using Matlab”, Cengage Learning,2014.

REFERENCES:

1. Poorna Chandra S, Sasikala. B ,Digital Signal Processing, Vijay Nicole/TMH,2013.

2. B.P.Lathi, ‘Principles of Signal Processing and Linear Systems’, Oxford University Press, 2010

3. Taan S. ElAli, ‘Discrete Systems and Digital Signal Processing with Mat Lab’, CRC Press, 2009.

4. Sen M.kuo, woonseng…s.gan, “Digital Signal Processors, Architecture, Implementations & Applications, Pearson,2013

5. Dimitris G.Manolakis, Vinay K. Ingle, applied Digital Signal Processing,Cambridge,2012

6. Lonnie C.Ludeman ,”Fundamentals of Digital Signal Processing”,Wiley,2013

IMPORTANT QUESTIONS	ANNA UNIVERSITY QUESTIONS	Subject Related PDF	Subject Related PPT
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EC6502 Principles of Digital Signal Processing

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UNIT V

Part A

1. What is Multirate digital signal processing?(May-2014,Nov-2011)
2. Write the different applications of Multirate DSP.(Nov-2013,2014)
3. What are the different areas in which Multirate DSP is used?
4. Give the advantages of Multirate DSP.
5. Define Decimation.(May-2012,Nov-2014,Nov-2010,May-2014)
6. Define Interpolation. .(May-2012)
7. What are the upsampling and downsampling process?(Nov-2011)
8. What is the need for sampling rate conversion?
9. What is the need for Multirate signal processing?
10. Give some examples of Multirate Digital system.
11. With an example explain the sampling process.
12. Draw the block diagram of Multirate stage decimator and interpolator.
13. Draw the block diagram of a general poly phase frame work for decimator and interpolator.
14. What is the need for Multistage filter implementation?

15.  What are the drawbacks in Multistage filter implementation. Obtain the poly phase structure of the filter with the transfer function.
                 H(z) = (1-3z^-1) / (1+4z^-1)

16. What are the advantages of poly phase decomposition

PART-B

1. State the applications of  Multirate Digital signal processing.(May-2014)
2. Explain with the block diagram, the general poly phase framework for interpolator and decimator.(Nov-2010,Nov-2014,May-2014,Nov-2013)
3. Explain about different applications of Multirate digital signal processing.
4. Explain about sampling rate conversion by a factor I/D.(May-2012)
5. Explain the poly phase decomposition for
   (i) FIR filter structure
   (ii) IIR filter structure
6. Explain in detail about Interpolation and decimation with Examples.(Apr-2011)
7. Explain in detail about Adaptive Channel Equalization.
8. Discuss on LMS adaptive filter.

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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
   

2. 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.                                                                                                   
3. 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. 
   

      

4. 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.                               
5. 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)

   

6. Express the following decimal numbers in binary form

            (a) 525    (b) 152.1875 (c) 225.3275

7. Express the decimal values 0.78125 and -0.1875 in (i) 1’s complement form (ii)sign magnitude form (iii) 2’s complement form.
8. 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
9. 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)

10. Derive the quantization input noise power and determine the signal to noise ratio of the system.  (Nov-2014)
11. Derive the truncation error and round off error noise power and compare both errors.
12. Explain product quantization error and coefficient quantization error with examples (Nov-2014,April-2011,May-2014)
13. Derive the scaling factor so that prevents the overflow limit cycle oscillations in a second order IIR system.
14. 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                                                                                   

15. Convert the following decimal numbers into binary:                     

(a) (20.675)     (b) (120.75)

16. 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)   
17. 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.

18. a. Write a short note on limit cycle oscillation.      (Nov-2010,Nov-2011)                                                                                                    b. Explain in detail about signal scaling.  ((Nov-2011,May-2012)
19. 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

20. 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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Unit – III

Part – A

1.   What are the desirable and undesirable features of FIR filter?

2.   Discuss the stability of the FIR filters.         

3.   What are the main advantages of FIR over IIR?

4.   What are the design techniques of designing FIR filters?

5.   What condition on the FIR sequence h(n) are to be imposed in order that this filter can be called a Linear phase filter?

6.    State the condition for a digital filter to be a causal and stable.

7.   What is Gibbs phenomenon?   (May-2014,Apr-2011)                              

8.   What are the properties of FIR filters?(Nov-2013,Nov-2011,Apr-2011)

9.   Explain the procedure for designing FIR filters using windows.   

10.     What is the principle of designing FIR filters using windows?

11.  What are desirable characteristics of windows? (Nov-2011,Nov-2013)

12.  What is a window and why it is necessary?

13.  Difference between FIR and IIR filters.                     

14.  Give the equation specifying Hanning and Blackman windows. (Nov-2014,2010)

15.  Draw the frequency response of N point Blackman window

16.  Draw the frequency response of N point Hanning window.     

17.     What is the necessary and sufficient condition for linear phase characteristics in FIR filter.

18.     Condition for the impulse response of FIR filters to satisfy for constant phase delay and group delay and only for constant group delay?

19.     Draw the direct form realization structure for FIR system.

20.     Direct form realization structure of a linear phase FIR system for N odd and N even.

21.     What are the advantages and disadvantages of FIR filters?

22.     Write the steps involved in FIR filter design.

23.     What are the possible types of impulse response for linear phase FIR filters?

24.     Write the magnitude and phase function of FIR filter when impulse response is symmetric and N is odd.

25.     Write the magnitude and phase function of FIR filter when impulse response is anti-symmetric and N is odd.

26.     Write the magnitude and phase function of FIR filter when impulse response is symmetric and N is even.

27.     Write the magnitude and phase function of FIR filter when impulse response is anti-symmetric and N is even.

28.     Write the procedure for designing FIR filter using Windows.

29.     What are the desirable characteristics of the frequency response of Window function?

30.     Compare the features of Hamming, Hanning and Blackman windows.

31.     Draw the Linear phse FIR filter for the following system function

       H(z)=1+2z^-1-3z^-2-4z^-3.             (Nov-2010,2014,May-2012)

Part – B

1.        Explain the need for the use of window sequences in the design of FIR filter. Describe the window sequences generally used and compare their properties. 

2.        Derive the frequency response of a linear phase FIR filter when impulse responses symmetric & order M is EVEN and ODD.

3.        Derive the frequency response of a linear phase FIR filter when impulse responses Anti-symmetric & order M is EVEN and ODD.

4.        A low pass filter has the desired response as given below

                 H_d(ω) =      e ^–j3ω       -π/8 ≤ ω ≤ π/2

                                    0             π/8 ≤ ω ≤ π

Determine the filter coefficients h(n) for M =7 using Hamming and Hanning window.(Nov-2013,Nov-2011)

5.        Design a LPF with 11 coefficients for the following specifications

Passband frequency edge=0.25 KHz

Sampling frequency=1 KHz

Using Hanning and Hamming window.

6.                                    A LPF is to be designed with the following desired frequency response

H_d(ω) =     e ^–j2ω       -π/4 ≤ ω ≤ π/4

                                 0             π/4 ≤ ω ≤ π

      

Determine the filter coefficients h(n) if the window function is defined as,             W[n] =   1         0≤n≤4

                             0         else

7.                                    Determine a HPF with  M =11 using Hamming  window

H_d(ω) =     1       π/4 ≤ ω ≤ π

                                     0       ω ≤ π/4

8.                                    Realize the FIR filters using sum of the two sub-signal polyphase decomposition

H(z) = 1 + 2z^-1 + (1/2)z^-2 – (1/2)z^-3 – (1/2)z^-4+ 2(1/2)z^-5 - 3(1/2)z^-6

9.                                    Realize the FIR filters in direct form

a.       H(z) = 1 + 2z^-1 + (1/2)z^-2– (1/2)z^-3 – (1/2)z^-4

b.      H(z) = 1 + 2z^-1 - 4z^-2+ z^-3 + 3z^-4

10.    Design a HPF using hamming window with a cut-off frequency of 1.2radians/sec and M =9.

11.    Design a band pass filter to pass frequencies in the range of 1 to 2 rad/sec using Hanning window with M =5.

12.    Design a band pass filter to pass frequencies in the range of 1.2 to 1.7 rad/sec using Blackman window with M =7.

13.    Obtain the Linear phase realization for the transfer function given below:

a.                     H(z) = 1 + (3/4)z^-1 + (17/8)z^-2+ (3/4)z^-3 + z^-4

b.    H(z) = (2/3) + z^-1 + (4/5)z^-2 + 3z^-3 + (7/8)z^-4

14.    Design an FIR filter to meet the following specification

Passband edge = 2 KHz

Stopband edge= 5 KHz

Stopband attenuation = 44dB

Sampling frequency = 20 KHz

15.                                If the desired response of a low-pass filter is

H_d(ω) =   e^-j3ω       -3π/4 < ω < 3π/4                                                    

                0            3π/4 < | ω | < π

     Determine H(ω) for M=7 using Frequency sampling tech.(Nov-2014,May-2014,2012)

16.                                Design a High pass filter using Hanning window to meet the following specifications.

     Cut-off frequency = 250 Hz                                                                                 

     Sampling frequency = 1 KHz

     Filter length = 7                                                                                          (Nov-2010)

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