Apparatus and method for sampling rate conversion with rational factors

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT For convenience, a glossary of terms used here and their definitions is provided prior to the claims.
Apparatus and method of the present invention are explained in the following order: (a) in the text, introducing conventions for a Z-transformation of signals; (b) by FIG.
1, illustrating data processing system 100; (c) by FIG.
2, illustrating signals x(t), X.
sub.
0 (T.
sub.
X) and Y.
sub.
0 (T.
sub.
Y) in system 100; (d) by FIG.
3, illustrating prior art rational decimation circuit 600; (e) by FIGS.
4-5, illustrating rational decimation circuit 200 of the present invention; (f) by FIG.
6, illustrating signal X.
sub.
n (T.
sub.
X) occurring in circuit 200; (g) by FIG.
7, illustrating signal V.
sub.
1 (T.
sub.
V) occurring in circuit 200; (h) by FIG.
8, illustrating signal spectra for explaining frequency transfer functions H.
sub.
XV (Z) and H.
sub.
VY (Z); (i) in the text, explaining a preferred FIR-function; (j) in the text, explaining further modifications of the FIR-function; (k) in the text in connection with tables I and II, explaining FIR-coefficients of the FIR-function; (l) explaining further details of the FIR-function; (m) in the text with table III and by FIG.
9, illustrating the generation of the FIR-coefficients; (n) by FIG.
10, illustrating a method of the present invention; and (o) further discussion of the present invention.
(a) A discrete time signal .
THETA.
(.
nu.
) has substantially constant magnitudes .
THETA.
during a discrete time interval T which is counted by .
nu.
.
Intervals T can be identified by other integer numbers, such as e.
g.
, T=0, T=1, T=2 and so on, or by indices, such as, e.
g.
, p, P, a, v, or .
gamma.
.
A Z-transform Z{.
THETA.
(.
nu.
)} of signal .
THETA.
(.
nu.
) can be calculated by: ##EQU1## wherein the z is the dimensionless Z-transformation operator.
The Z-transformation operator is described, for example, in section 3.
1 ("The Z-transform") of ?2!.
The notation z(-.
nu.
) represents the function z.
sup.
-.
nu.
.
This convention is used hereafter