Table of Contents

1. Introduction

2. Discrete-Time Simulation of First-Order Response

2.1 Background

2.2 Optimum First-Order Simulation

2.2.1 Basic Assumptions

2.2.2 General First-Order Recurrence Formulas

2.2.3 Optimum Recurrence Coefficients for Constant t

2.2.4 Optimum Recurrence Coefficients for Variable t

2.2.5 Discussion

2.3 Modified First-Order Simulation Methods

2.3.1 Simplifications Based on Approximations of ez

2.3.2 Finite Differences and Bilinear Substitution

2.3.3 Pre-Warping

2.3.4 Composite Past Value Recurrence

2.3.5 Discussion

3. Discrete-Time Simulation of Second-Order Response

3.1 Background

3.2 Optimum Second-Order Recurrence Formulas

3.2.1 Basic Assumptions

3.2.2 General Second-Order Recurrence Formulas

3.2.3 Optimum Recurrence Coefficients for Second-Order Interpolation

3.2.4 Optimum Recurrence Coefficients for Point-to-Point Interpolation

3.2.5 Discussion

3.3 Modified Methods for Second Order Simulation

3.3.1 Cascaded First-Order Simulations

3.3.2 Finite Difference Method

3.3.3 Bilinear Substitution

3.3.4 Simplifications Based on Approximations of ez

3.3.5 Discussion

APPENDIX A: Recursive Simulation of Feedback Loops

APPENDIX B: Discrete-Time Simulation of Nth-Order Response