DESIGN AND ANALYSIS OF ANALOG FILTERS A Signal ...

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96 DESIGN AND ANALYSIS OF ANALOG FILTERS: The corresponding phase response and magnitude frequency response for (2.108) and (2.109) with and are shown in Figures 2.40 and 2.41, respectively. Note that the group delay is a constant for this example, over the frequency range of and is also a constant of zero outside that range. Obtaining the phase response from the magnitude frequency response for practical filters is very difficult to do using Hilbert transform relations. A more practical approach for practical filters would be to use the Analog Filter Design Chapter 2 Analog Filter Design and Analysis Concepts
A Signal Processing Perspective 97 Theorem and the method developed in Section 2.7: given the magnitude-squared frequency response, obtain the minimum-phase transfer function H(s), 21 from which is readily found. For example, the simple one-pole lowpass filter of Example 2.18, on page 62, beginning with the magnitude-squared frequency response of readily yields the H(s) of l/(s + 1), from which However, for this simple problem, which is difficult to evaluate in (2.102) to find the phase. Therefore, the Hilbert transform method is of primary value in theoretical analysis, such as done in the above examples. In Example 2.27, as indicated in the example, the results give further evidence that the ideal lowpass response can not be realized, and can therefore only be approximated. Also, Example 2.28 yields the magnitude frequency response for a desired linear-phase response over a given frequency range. The theoretical result suggests that to approximate the linear phase response, the resulting magnitude frequency response must be approximated. As will be seen in Chapter 7, Bessel filters, indirectly, do approximate this response. 21 Actually, as noted in Section 2.7, the resultant H(s) is not restricted to be minimum phase. Therefore, the procedure can identify various phase realizations, assuming there are finite-valued transfer function zeros with non-zero real parts. Section 2.15 Hilbert Transform Relations
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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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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 8 OTHER FILTERS In this cha
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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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