viii CONTENTS 3.4 FIR and IIR Filters,105 3.5 Causality and Stability,112 3.6 Problems.117 4 FIR Filtering and Convolution 121 4.1 Block Processing Methods,122 4.1.1 Convolution,122 4.1.2 Direct Form,123 4.1.3 Convolution Table,126 4.1.4LTΠFom,127 4.1.5 Matrix Form,129 4.1.6 Flip-and-Slide Form,131 4.1.7 Transient and Steady-State Behavior,132 4.1.8 Convolution of Infinite Sequences,134 4.1.9 Programming Considerations,139 4.1.10 Overlap-Add Block Convolution Method,143 4.2 Sample Processing Methods,146 4.2.1 Pure Delays,146 4.2.2 FIR Filtering in Direct Form,152 4.2.3 Programming Considerations,160 4.2.4 Hardware Realizations and Circular Buffers,162 4.3 Problems,178 5 Z-Transforms 183 5.1 Basic Properties,183 5.2 Region of Convergence,186 5.3 Causality and Stability,193 5.4 Frequency Spectrum,196 5.5 Inverse z-Transforms,202 5.6 Problems,210 6 Transfer Functions 214 6.1 Equivalent Descriptions of Digital Filters,214 6.2 Transfer Functions,215 6.3 Sinusoidal Response,229 6.3.1 Steady-State Response,229 6.3.2 Transient Response,232 6.4 Pole/Zero Designs,242 6.4.1 First-Order Filters,242 6.4.2 Parametric Resonators and Equalizers,244 6.4.3 Notch and Comb Filters,249 6.5 Deconvolution,Inverse Filters,and Stability,254 6.6 Problems,259viii CONTENTS 3.4 FIR and IIR Filters, 105 3.5 Causality and Stability, 112 3.6 Problems, 117 4 FIR Filtering and Convolution 121 4.1 Block Processing Methods, 122 4.1.1 Convolution, 122 4.1.2 Direct Form, 123 4.1.3 Convolution Table, 126 4.1.4 LTI Form, 127 4.1.5 Matrix Form, 129 4.1.6 Flip-and-Slide Form, 131 4.1.7 Transient and Steady-State Behavior, 132 4.1.8 Convolution of Infinite Sequences, 134 4.1.9 Programming Considerations, 139 4.1.10 Overlap-Add Block Convolution Method, 143 4.2 Sample Processing Methods, 146 4.2.1 Pure Delays, 146 4.2.2 FIR Filtering in Direct Form, 152 4.2.3 Programming Considerations, 160 4.2.4 Hardware Realizations and Circular Buffers, 162 4.3 Problems, 178 5 z-Transforms 183 5.1 Basic Properties, 183 5.2 Region of Convergence, 186 5.3 Causality and Stability, 193 5.4 Frequency Spectrum, 196 5.5 Inverse z-Transforms, 202 5.6 Problems, 210 6 Transfer Functions 214 6.1 Equivalent Descriptions of Digital Filters, 214 6.2 Transfer Functions, 215 6.3 Sinusoidal Response, 229 6.3.1 Steady-State Response, 229 6.3.2 Transient Response, 232 6.4 Pole/Zero Designs, 242 6.4.1 First-Order Filters, 242 6.4.2 Parametric Resonators and Equalizers, 244 6.4.3 Notch and Comb Filters, 249 6.5 Deconvolution, Inverse Filters, and Stability, 254 6.6 Problems, 259