The DW state-space model is given in terms of the FDTD state-space
model by Eq. (32). The similarity transformation matrix
is
bidiagonal, so that
and
are both approximately
diagonal when the output is string displacement for all . However,
since
given in Eq. (12) is upper triangular, the input matrix
can replace sparse input matrices
with only
half-sparse
, unless successive columns of
are equally
weighted, as discussed in §4. We can say that local
K-variable excitations may correspond to *non-local* W-variable
excitations. From Eq. (36) and Eq. (37), we see that
*displacement inputs are always local in both systems*.
Therefore, local FDTD and non-local DW excitations can only occur when
a variable dual to displacement is being excited, such as velocity.
If the external integrator Eq. (38) is used, all inputs are
ultimately displacement inputs, and the distinction disappears.

Download wgfdtd.pdf

Copyright ©

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

[Automatic-links disclaimer]