Page  191 ï~~A Real-Time Implementati Frederick L. Malouf Apple Computer, Inc. 20525 Mariani Ave. MS: 71AB Mark Lentczn Braying at the 1209 Villa St. Mountain Vie Cupertino, CA 95014 malouf@ apple.com ABSTRACT: A new approach to Physical N main objectives are unification of different ty and string models), unification of static exten sounds) and internal dynamic signals (delay 1 in real time on modem signal processors. Th and two example instruments are presented. We set out to implement Physical Modeling s

Page  192 ï~~In many instances the functional part of the junction va (4) aj =A *K Our equation (1) easily implements the clarinet model i cannot be expressed in the form of equation (1). We st create an equivalent model. To clarify the difference, t while the t' stands for theirs (Smith's). We start with the following difference: (5a,b) Ao w 0 + + b+./ where a' and b' are the velocity inputs from the string (5a) is in the form of equation (3). theirs has a subtraction. These eq We sum the inputs uations lead us to ass (6a,b) wo -'Vt L The. n tirnit Pnintinnv chn the f inrinmontcl r li/frreonrrJ

Page  193 ï~~sampled signals (envelopes for mouth pressure or I consistent interface allows us to freely interchange without altering the implementation of the junction The delay line interface consists of input an sample. A simple delay line shifts the samples, pr A function source, which may be an envelope or sa output while ignoring its input. Sample input and c lines with the side effect of reading an AiD or writ Filters are implemented as special form of d delay memory are convolved with a set of coefficil used in conjunction with another form of delay line filter' output (or its opposite: high pass if the filte We close with two examples of how these e