Parallel Impedance Biquads

In the current situation, computing the junction-velocity
from the incoming waves
using the parallel biquad expansion
Eq.(C.104) for
, we split each term
of Eq.(C.102) into its *instantaneous* and *delayed*
components [25]:^{C.12}

so that

where | (C.109) | ||

and | (C.110) | ||

(C.111) |

Define

and | (C.112) | ||

(C.113) |

Then Eq.(C.97) can be written

(C.114) | |||

(C.115) | |||

(C.116) |

This structure can be realized as shown in Fig.C.30 and derived above. This form is convenient for encoding in FAUST [471]. Here, denotes the sum of all incoming wave impedances plus the

More directly derived, we can write Eq.(C.97) as

or | (C.117) | ||

(C.118) |

This expression can be taken by inspection to the time domain in terms of the parallel biquads to yield the following difference equation:

and and , as in Eq.(C.108) above.

[How to cite this work] [Order a printed hardcopy] [Comment on this page via email]

Copyright ©

Center for Computer Research in Music and Acoustics (CCRMA), Stanford University