Method for inharmonic tone generation using a coupled mode digital filter

DETAILED DESCRIPTION A block diagram of a preferred embodiment of the invention is shown in FIG.
5.
It includes a collection of m first order allpass (FOAP) filters 28(1), 28(2), .
.
.
, 28(m) and a collection of m corresponding unit delay elements 30(1), 30(2), .
.
.
, 30(m).
As shown in FIG.
5, the FOAP and unit delay pairs are arranged with corresponding adders 31(1), 31(2), .
.
.
, 31(m) to form a collection of m negative feedback loops 32(1), 32(2), .
.
.
, 32(m) corresponding to the m modes being simulated.
As described in detail below, each of these loops forms a lossless oscillator having a characteristic resonant frequency, and is effectively a novel implementation of a second order filter.
In the preferred embodiment, the mode oscillator loops 32(1), 32(2), .
.
.
, 32(m) are initially excited by a common excitation input signal entering the circuit at an adder 33.
Signals from loops 32(1), 32(2), .
.
.
, 32(m) are then coupled in an adder 34 which sends a coupled mode signal out of the circuit.
The coupled mode signal is also sent to a coupling filter 36 which controls the decay envelope for the synthesized sound.
The attenuated signal then passes through adder 33 and is fed back into the bank of m mode oscillator loops.
FOAP filters 28 have transfer functions of the form: ##EQU2## These m filters may be computed with a set of m corresponding difference equations, for example: ##EQU3## where n is the time sample index, y.
sub.
1 (n), y.
sub.
2 (n), .
.
.
, y.
sub.
m (n) are the respective output signals of filters 28(1), 28(2), .
.
.
, 28(m), and x.
sub.
1 (n), x.
sub.
2 (n), .
.
.
, x.
sub.
m (n) are the respective input signals of the filters.
The FOAP coefficients, a.
sub.
1, a.
sub.
2, .
.
.
, a.
sub.
m, determine the tuning of the m modal frequencies of the coupled mode digital filter.
In the non-decaying case, where the coupling filter will have a gain of 0 for all frequencies, the correct tuning of the resonant modes may be determined as follows.
Consider a single negative feedback loop containing a FOAP filter with transfer function ##EQU4## and a delay element with transfer function D(z)=z