DESIGN AND ANALYSIS OF ANALOG FILTERS A Signal ...

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212 DESIGN AND ANALYSIS OF ANALOG FILTERS: 6. 25 Repeat Problem 6.24 for the Shaping Factor with a = 3 dB and b =60 dB. That is, suppose the following filter specifications are given: (a) (b) (c) (d) and N = 6. Determine the value of the Shaping Factor for a Chebyshev Type II filter with the given specifications. Determine the value of the Shaping Factor for a Butterworth filter with similar specifications: and N = 6. Compare the above values with the value of the Shaping Factor for a Chebyshev Type I filter with similar specifications: and N = 6. Compare the above values with the value of the Shaping Factor for an elliptic filter with similar specifications: and N = 6. 6. 26 Suppose filter specifications are stated as follows: Determine the required filter order to meet the given specifications: (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) For an elliptic filter with and For an elliptic filter with and For an elliptic filter with and For an elliptic filter with and For comparison purposes, repeat parts (a) through (d) for a Butterworth filter For comparison purposes, repeat parts (a) through (d) for a Chebyshev Type II filter For comparison purposes, repeat parts (a) through (d) for an elliptic filter, but with For comparison purposes, repeat parts (a) through (d) for an elliptic filter, but with For comparison purposes, repeat parts (a) through (d) for an elliptic filter, but with For comparison purposes, repeat parts (a) through (d) for a Chebyshev Type I filter with 0. 1 dB of ripple. For comparison purposes, repeat parts (a) through (d) for a Chebyshev Type I filter with 0. 5 dB of ripple. For comparison purposes, repeat parts (a) through (d) for a Chebyshev Type I filter with 1. 5 dB of ripple. 6. 27 By making use of the scaling property of Fourier transforms and Figure 6. 17, determine, for a tenth-order elliptic filter with approximate values for the following: (a) The time at which the unit impulse response is a maximum. Chapter 6 Elliptic Filters
A Signal Processing Perspective 213 (b) (c) (d) The amplitude of the unit impulse response maximum. The half-value width of the unit impulse response, defined as the time during which The duration, of the unit impulse response, defined as the time from 6. 28 Repeat Problem 6. 27 for 6. 29 Sketch the step response of a 10th- order elliptic filter with and Refer to Figure 6. 18 and make use of the scaling property of Fourier transforms. What would the maximum group delay be for this filter, and at what frequency would it occur? At what time would the peak of the unit impulse response of this filter be, and what would be the value of that peak? 6. 30 Suppose an anti-aliasing filter is needed prior to an analog-to-digital converter to be used in a speech processing system. Suppose a sampling rate of 8000 samples/s is to be used, and therefore it is decided that the anti-aliasing filter should have a minimum attenuation of 60 dB at 4000 Hz. elliptic filter is to be used. Suppose an (a) If and what is the minimum order (b) required? If and N= 10, what is maximum value of (c) If and N= 10, what is the minimum value of 6. 31 Under the conditions of part (c) of Problem 6. 30, determine the transfer function H(s), and give numerical values for all the poles and zeros. 6. 32 Using the MATLAB functions ellipap, impulse and step: (a) Determine the transfer function in polynomial form, and also factored to indicate the poles and zeros, of an elliptic filter with and N = 6. (b) Determine the impulse response and the step response for the filter of part (a). (c) By multiplying the pole vector and the zero vector found in part (a) by determine the transfer function of an elliptic filter with and N = 6. (d) Determine and plot the magnitude frequency response of the filter of part (c) by using the MATLAB function freqs. Use a vertical scale in dB and a linear horizontal scale from 0 to 5000 Hz. Also determine and plot the phase response over this same frequency range. Use the MATLAB function unwrap rather than plotting the principle phase. Section 6. 12 Chapter 6 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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130 (f) (g) (h) DESIGN AND ANALYSIS
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CHAPTER 5 CHEBYSHEV TYPE II FILTERS
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CHAPTER 10 PASSIVE FILTERS In this
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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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