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FIR Filters - Contents

The design is synthesized on the target device Spartan 3-3s200ft256-4. At first optimization goal is kept as speed. Then the number of slices used is 144 out of 1920(7%). Number of Slice Flip Flops used are125 out of 3840(3%). Number of 4 input LUTs are 261 out of 3840(6%). Total number of bonded IOBs used are 83 out of 173(47%).1 out of 8(12%) global clock is also used. As per timing analysis, maximum frequency of operation is 104.188 MHz. | Digital Filter Designer s Handbook Featuring C Routines C. Britton Rorabaugh TAB Books Division of McGraw-Hill Inc. Blue Ridge Summit PA 17294-0850 Contents List of Programs xi Preface xv Chapter 1. Mathematical Review 1 1.1 Exponentials and Logarithms 1 1.2 Complex Numbers 4 1.3 Trigonometry 6 1.4 Derivatives 12 1.5 Integration 13 1.6 Dirac Delta Function 14 1.7 Mathematical Modeling of Signals 17 1.8 Fourier Series 22 1.9 Fourier Transform 28 1.10 Spectral Density 31 Chapter 2. Filter Fundamentals 35 2.1 Systems 35 2.2 Characterization of Linear Systems 39 2.3 Laplace Transform 41 2.4 Properties of the Laplace Transform 43 2.5 Transfer Functions 45 2.6 Heaviside Expansion 47 2.7 Poles and Zeros 48 2.8 Magnitude Phase and Delay Responses 51 2.9 Filter Fundamentals 53 Chapter 3. Butterworth Filters 65 3.1 Transfer Function 65 3.2 Frequency Response 66 3.3 Determination of Minimum Order for Butterworth Filters 70 vll viii Contents 3.4 Impulse Response of Butterworth Filters 70 3.5 Step Response of Butterwoth Filters 72 Chapter 4. Chebyshev Filters 77 4.1 Transfer Function 78 4.2 Frequency Response 83 4.3 Impulse Response 86 4.4 Step Response 86 Chapter 5. Elliptical Filters 93 5.1 Parameter Specification 93 5.2 Normalized-Transfer Function 95 5.3 Denormalized-Transfer Function 99 Chapter 6. Bessel Filters 109 6.1 Transfer Function 109 6.2 Frequency Response 111 6.3 Group Delay 111 Chapter 7. Fundamentals of Digital Signal Processing 117 7.1 Digitization 117 7.2 Discrete-Time Fourier Transform 127 7.3 Discrete-Time Systems 129 7.4 Diagramming Discrete-Time Systems 131 Chapter 8. Discrete Fourier Transform 137 8.1 Discrete Fourier Transform 137 8.2 Properties of the DFT 139 8.3 Implementing the DFT 141 8.4 Fast Fourier Transforms 141 8.5 Applying the Discrete Fourier Transform 143 Chapter 9. The z Transform 151 9.1 Region of Convergence 151 9.2 Relationship between the Laplace and z Transforms 155 9.3 System Functions 155 9.4 Common -Transform Pairs and Properties 156