DESIGN AND ANALYSIS OF ANALOG FILTERS A Signal ...

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268 DESIGN AND ANALYSIS OF ANALOG FILTERS: 8.15 8.16 8.17 8.18 In Problem 8.8 the Legendre polynomials ( m = 0) are found for orders 2, 3,4, 5, and 6. Show that these same polynomials are obtainable as special cases of In Problem 8.9 the modified first-associated Legendre polynomials are found for orders 1, 2, 3, 4, and 5. Show that these same polynomials are obtainable as special cases of In Problem 8.10 the modified second-associated Legendre polynomials are found for orders 1,2, 3, and 4. Show that these same polynomials are obtainable as special cases of By making use of special cases of determine the modified thirdassociated Legendre polynomials of orders 3 and 4. 8.19 Subjectively compare the performance of a 10th-order ultraspherical filter with and as shown in Figures 8.22 through 8.28, with that of a 10th-order Chebyshev Type I filter with 1 dB of ripple and as shown in the figures in Chapter 4. In your judgment, what are the advantages and disadvantages of each filter compared with the other? Plot the poles of each filter, on the same graph for ready comparison. 8.20 Determine the polynomial associated with a 5th-order Papoulis filter. 8.21 8.22 8.23 Determine the polynomial associated with a 6th-order Papoulis filter. Given that determine the Filter Selectivity of a 4th-order Papoulis filter when Compare this numerical value with that of a 4th-order Butterworth filter with Compare this numerical value with that of a 4th-order Chebyshev Type II filter with and Compare this numerical value with that of a 4th-order Chebyshev Type I filter with and Interpret the numerical results of this problem and discuss the significance of them. Show that the Papoulis filter becomes identical to the Butterworth filter when approaches the limit of zero and, simultaneously, is maintained normalized to unity. It is sufficient to show this for the 4th-order case. 8.24 Determine the polynomial associated with a 4th-order Halpern filter. 8.25 Determine the polynomial associated with a 5th-order Halpern filter. Chapter 8 Other Filters
A Signal Processing Perspective 269 8.26 Given that a = 3dB, and b= 100 dB, determine the Shaping Factor of a 4th-order Halpern filter when Compare this numerical value with that of a 4th-order Butterworth filter with Compare this numerical value with that of a 4th-order Chebyshev Type II filter with and Compare this numerical value with that of a 4th-order Chebyshev Type I filter with and Interpret the numerical results of this problem and discuss the significance of them. 8.27 8.28 Compare the performance of the Halpern filter, as shown in Figures 8.36 through 8.42, with that of the related Papoulis filter, as shown in Figures 8.29 through 8.35. In your judgment, what are the advantages and disadvantages of each filter compared with the other? Plot the poles and zeros of the 4th-order phase-compensated 10th-order Butterworth filter, as presented in Section 8.7. 8.29 Extend the work shown in Section 8.7 by designing, by trial an error, a 6thorder phase-compensation filter to cascade with the 10th-order Butterworth filter to improve performance over that of the 4th-order phase-compensated filter. Start with the given 4th-order all-pass filter, i.e., add an additional 2ndorder all-pass. Select the 2nd-order all-pass filter parameters to yield improved group delay performance. You may use as a starting point the MATLAB mfile F8_45dat.m on the accompanying disk. Plot graphs similar to Figures 8.43 through 8.47 that include the results of the 6th-order phase compensation. Also plot a graph of the poles and zeros of the 6th-order phase-compensated 10th-order Butterworth filter. Section 8.8 Chapter 8 Problems
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DESIGN AND ANALYSIS OF ANALOG FILTE
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Design and Analysis of A Signal Pro
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PREFACE nalog filters, that is cont
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The term “approximation” is use
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PREFACE Chapter 1. 2. INTRODUCTION
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6.7 6.8 6.9 6.10 6.11 6.12 TABLE OF
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CHAPTER 1 INTRODUCTION Iimportance
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CHAPTER 2 ANALOG FILTER DESIGN AND
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114 DESIGN AND ANALYSIS OF ANALOG F
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130 (f) (g) (h) DESIGN AND ANALYSIS
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CHAPTER 5 CHEBYSHEV TYPE II FILTERS
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6. 1 INTRODUCTION CHAPTER 6 ELLIPTI
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CHAPTER 7 BESSEL FILTERS Although a
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CHAPTER 10 PASSIVE FILTERS In this
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APPENDIX B CONTENTS OF THE ACCOMPAN
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APPENDIX D THE MATLAB m-FILE EXAMP6
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A Active filters, 359-390 advantage
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