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 – 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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Unit – II

Part – A

1.      Distinguish between analog and digital filter.

2.      What are the advantages of digital filter over analog filter?

3.      Give the Magnitude function of Butterworth filter. What is the effect of varying order of N on magnitude and phase response?

4.      Give any two properties of Butterworth low pass filter.

5.      What are the properties of chebyshev filter?(Apr-2011,Nov-2011)

6.      Give the equation for the order N and cut off frequency Ω_c of Butterworth filter.

7.      Given the specification α_p = 1dB; α_s = 30dB; Ω_p = 200 rad/sec; Ω_s = 600 rad/sec. Determine the order of the Butterworth filter. (Ans: N = 4)

8.      Give the chebyshev filter transfer function and its magnitude response.

9.      Distinguish between the frequency response of Chebyshev type I and type II filters.

10.  Give the equation for the order N of Chebyshev filter.

11.  Given the specification α_p = 3dB; α_s = 16dB; f_p = 1KHz; f_s = 2KHz. Determine the order of the Chebyshev filter. (Ans: N = 2)

12.  Distinguish between Butterworth and Chebyshev (type I) filters.

13.  How one can design digital filters from analog filters

H(s) =      (s + 0.2)      

                                    (s + 0.2)² + 9

Use the impulse invariant technique. Assume T = 1s.

            Ans:     H(z) =              1 + 0.811z^-1                

                          (1+ 1.621 z^-1+ 0.671 z^-2)

14.  For the analog transfer  function

H(s) =           1            

                                     (s + 1) (s + 2)

Determine H(z) using impulse invariant technique. Assume T = 1s.(Nov-2011)

Ans:     H(z) =                  0.2326z^-1                

               (1 - 0.503z^-1 + 0.0498 z^-2)

15.  Mention any two procedure for digitizing the transfer function of an analog filter?(Nov-2013)

16.  What are the properties that are maintained same in the transfer of analog filter into a digital filter?

17.  What is meant by impulse invariant method of designing IIR filter?

18.  By impulse invariant method obtain the digital filter transfer function and the differential equation of analog filter H(s) = 1/(s + 1).

19.  Obtain the impulse response of digital filter corresponding to an analog filter with impulse response h_a(t) = 0.5e^-2t u(t) and with a sampling rate of 1Hz using impulse invariant method.

20.  Why impulse invariant method is not preferred in the design of IIR filter other than low pass filter?

21.  Give the bilinear transformation equation between s-plane and z-plane.

22.  Using bilinear transformation obtain H(z) if H(s) = 1 / (s + 1)² and T = 0.1s.             

Ans:     H(z) =      0.0476(1 + z^-1)²      

                            (1 - 0.9048 z^-1)²

23.  What are the properties of the bilinear transformation?

24.  What is warping effect?

25.  Write short notes on prewarping. (Nov-2014,Nov-2010,May-2012)

26.  Distinguish between recursive and non-recursive realisation.

27.  What are the advantages and disadvantages of bilinear transformation?(May-2014)

28.  What are the different types of realization structures for realisation of IIR systems?

29.  Draw the general realization structure in direct form I and II of IIR system.

30.  Give direct form I and direct form II structure of 2^nd order system.

31.  How many number of addition, multiplication delay blocks are required to realize a system H(z) having M zeros and N poles in (a) direct form I and (b) direct form II realization?

32.  What is the main advantage of direct form II realization when compared to direct form I realization?(Nov-2011,Nov-2013,Nov-2010)

33.  What is transposed structure?

34.  Give the transposed direct form II structure of IIR 2^nd order.

35.  Realize y(n) + y(n-1) + 0.25y(n-2) = x(n) in cascade form.

36.  What is the advantage of cascade realization? (Hint: Quantization error can be reduced).

Part – B

1.      Design an analog Butterworth filter that has a -2dB of passband attenuation at a frequency of 20 rad/sec and atleast -10dB stopband attenuation at a frequency of 30 rad/sec.

Ans:     N = 4

 H(s) =                             0.2092 x 10⁶                                               

                               (s² + 16.389s + 457.394) (s²+ 39.518s + 457.394)

2.      For the given specifications, design an analog Butterworth filter,

0.9 <|H(jΩ)| < 1,         0 <Ω < 0.2π

|H(jΩ)| <0.2,               0.4π < Ω <π

Ans:     N = 4

 H(s) =                                 0.323                                          

                                                  (s² + 0.577s + 0.0576π²) (s² + 1.393s + 0.0576π²)

3.      Design a Chebyshev filter with a maximum passband attenuation of 2.5dB at Ω_p = 20rad/sec and stopband attenuation of 30dB at Ω_p = 50rad/sec.

Ans:     N = 3

 H(s) =                     2265.27              

                                                  (s + 6.6) (s²+ 6.6s + 343.2)

4.      Using impulse invariant method with T = 1s, determine H(z) if H(s) = 1/( s²+√2s+1).

Ans:     H(z) =                0.453z^-1                    

                                      (1 – 0.7497 z^-1+ 0.2432 z^-2)

5.      For the analog transfer function H(s) = 2 / (s+1)(s+2), determine H(z) using impulse invariance method. Assume T=1s.

Ans:     H(z) =                0.465z^-1                    

                          (1 – 0.503 z^-1+ 0.05 z^-2)

6.      Design a 3^rd order Butterworth digital filter using impulse invariant technique. Assume sampling period T = 1s.(Nov-2011)

Ans:     H(z) =          1               +         (-1 + 0.453z^-1)           

(1 – 0.368z^-1)       (1 – 0.786 z^-1+ 0.368 z^-2)

7.      An analog filter has a transfer function H(s) = 10 / (s² + 7s + 10). Design a digital filter equivalent to this using impulse invariant method for T = 0.2s.

Ans:     H(z) =                0.201z^-1                    

                          (1 – 1.378 z^-1+ 0.247 z^-2)

8.      Apply bilinear transformation to H(s) = 2 / (s+1)(s+2) with T = 1s and find H(z).

Ans:     H(z) =   0.166 (1+z^-1)²

             (1 – 0.33 z^-1)

9.      Determine H(z) that results when the bilinear transformation is applied to

H(s) =         (s² +4.525)          

                                      (s² + 0.692s + 0.504)

Ans:     H(z) =  1.448 + 0.1783z^-1 + 1.448z^-2  

                         (1 – 1.1875 z^-1+ 0.5299 z^-2)

10.  Obtain the direct form I an direct form II realization structure for the system described by the following difference equation

1. y(n) = 0.5 y(n-1) – 0.25 y(n-2) + x(n) + 0.4 x(n-1).
2. y(n) = -0.1 y(n-1) + 0.72 y(n-2) + 0.7x(n) - 0.252 x(n-2).

11.  Obtain the direct form I, direct form II, cascade and parallel form realization for the system y(n) = -0.1 y(n-1) + 0.2 y(n-2) + 3x(n) + 3.6 x(n-1) + 0.6 x(n-2).(Nov-2011,Nov-2014,May-2014,Nov-2010,May-2012)

12.  Obtain the cascade and parallel realization for the following systems

1. H(z) =  (1 + 1.5z^-1 + 0.5z^-2) ( 1 - 1.5z^-1 + z^-2)  

          (1 + z^-1 + 0.25z^-2) ( 1 + 0.25z^-1 + 0.5z^-2)           

2. H(z) =               (1 - 0.5z^-1) ( 1 - 0.5z^-1 + 0.25z^-2)                    

           (1 + 0.25z^-1) (1 + z^-1 + 0.5z^-2) ( 1 - 0.25z^-1 + 0.5z^-2)

13.  Design a digital Butterworth filter satisfying the constraint(Nov-2011,May-2012)

0.707 < |H(jΩ)| < 1,     0 <Ω < π/2

|H(jΩ)| < 0.2,               3π/4 <Ω < π

With T=1s using (a) Bilinear transformation (b) impulse invariant. Realize the fiter in each case using the most convenient realization form.

(a) Ans:           N = 2

 H(s) =            4          

                                                            (s² + 2.828s + 4)

                        H(z) =   0.293 (1+z^-1)²

             (1 + 0.172z^-1)

(b) Ans:           N = 4

H(s) =                              (1.57)⁴                                

                                     (s² + 1.202s + 2.465) (s² + 2.902s + 2.465)

H(z) =        (1.454 + 0.184z^-1)       +    (-1.454 + 0.231z^-1)     

(1 – 0.387 z^-1 + 0.055 z^-2)     (1 – 0.132 z^-1 + 0.301 z^-2)

14.  Design a Chebyshev low pass filter with specifications α_p = 1dB ripple in the passband 0 ≤ ω ≤ 0.2π, α_s= 15dB ripple in the stopband 0.3π ≤ ω ≤ π, using (a) bilinear transformation and (b) impulse invariant method.(Nov-2014,Nov-2010)

(a) Ans:           N = 4

H(s) =                              0.0438                                

                                   (s² + 0.1814s + 0.4165) (s² + 0.4378s + 0.118)

H(z) =                           0.0018(1 + z^-1)⁴                                 

 (1 – 1.499 z^-1 + 0.848 z^-2) (1 – 1.555 z^-1 + 0.649 z^-2)

(b) Ans:           N = 4

H(s) =                              0.0383                                

                                       (s² + 0.175s + 0.391) (s² + 0.423s + 0.11)

H(z) =        (-0.083 - 0.025z^-1)       +    (0.083 + 0.0238z^-1)    

 (1 – 1.49 z^-1 + 0.839z^-2)      (1 – 1.56 z^-1 + 0.655 z^-2)

15.  Design a digital Chebyshev filter to satisfy the constraint

0.707 < |H(jΩ)| < 1,     0 <Ω < 0.2π

|H(jΩ)| < 0.1,               0.5π <Ω < π

            Using bilinear transformation and assuming T = 1s.

Ans:                 N = 2

H(s) =                  0.2111                    

                                          (s² + 0.418s + 0.2985)

H(z) =              0.041(1 + z^-1)²            

  (1 – 1.4418 z^-1 + 0.6743 z^-2)

16.  Discuss the steps in the design of IIR filter using BLT method.(Nov-2013,May-2012)

17.  Determine H(z) for a Butterworth filter satisfying the following

√0.5 <|H(jΩ)| < 1,      0 <Ω < π/2

|H(jΩ)| < 0.2,               3π/4 <Ω < π

            With T = 1s. Apply impulse invariant transformation.

Ans:                 N = 4

H(s) =                              6.086                                  

                                     (s² + 1.2022s + 2.467) (s² + 2.903s + 2.467)

H(z) =        (-1.451 - 0.232z^-1)       +       (1.451 + 0.185z^-1)   

 (1 – 0.131 z^-1 + 0.301z^-2)    (1 – 0.386 z^-1 + 0.055 z^-2)

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