
XI - ANNEXEA
XI.1 - IIR FILTEROPERATION
Each IIR filtering section included in the ST7544
can performup to sevenbiquadratictransfer func-
tions in cascade, operating at four times the sam-
pling frequency(see FigureA1).
Eachbiquad isdefinedby fivecoefficients,A,B, C,
D and E (see Figure A2). An additional coefficient
,F, scales the IIR filter output.
Unused biquads are made transparent by pro-
gramming A to one and the four remaining coeffi-
cients to zero. Such biquads should preferablybe
located in the first sectionsof the IIR filter in order
to reduce the calculation noise.
XI.1.1- CoefficientRounding
Initially, coefficientsof thefilter to be implemented
must be exclusively between +2 and -2. To derive
theactualusable12+1bit coefficients,therounding
processdescribedinFigureA3 mustbeperformed.
Each 13 bit coefficient K is split into its doubling
factor K2, and its 12 bit basicvalue K1, as the IIR
architectureworkswith12 bitcoefficientsanduses
an extra accumulationwhen coefficientdoublingis
needed.
K2
∈
[0,1]and -2
12
< K1< +2
12
The coefficients are loaded into the different IIR
filtersthrough 16 bit widetime slots. The formatto
be used is as follows :
MSB
K2
(1 bit)
<--------- 16 bit word -------->
Toprogrammeone IIRfilter it is necessaryto send
Figure A1 :
IIR Filter Diagram
K1
(12-bit)
LSB
0 0 0
(3-bit)
five words per biquad followed by two additional
words setto zeroand the F coefficientword :
B(1), C(1), A(1), D(1), E(1), B(2),..., E(7), 0000
H
,
0000
H
, F
The total number of words sent is therefore 38.
XI.1.2- DetailedOperation
The architecture of the device supporting the IIR
filterisbasedon28bitdatapath.Thebasicfunction
is as follows: one coefficient K(N) is multipled by
one sample X(N) followed by one accumulation
withvalue clampling.It can be preciselydescribed
as follows :
FUNCTION PAC
K(N), X(N), S
LOCAL
P
P =
TRUNC
(K1(N)x X(N)/2
12
)
S = S + P
IF ABS
(S) > 2
27
THEN
IF SIGN
(S) > 0
THEN CLAMP
S
TO
2
27
-1
ELSE CLAMP
S
TO
2
27
IF
K2(N) = 1
THEN
S = S + P
IF ABS
(S) > 227
THEN
IF SIGN
(S) > 0
THEN CLAMP
S
TO
2
27
-1
ELSE CLAMP
S
TO
2
27
END OF FUNCTION
The TRUNC function is a two’s complement trun-
cature.
As previously mentionned, the second accumula-
tion is controlledby the doublingfactor K2(N).
The complete process of computing 16 bit output
samples (V
OUT
) from 16 bit input samples (V
IN
)
appearsin FigureA4.
BIQUAD#1
IN
V
(1)
V
(1)
OUT
212
F
IN
V
IN
OUT
IN
OUT
BIQUAD#2
V
(2)
V
(2)
OUT
V
BIQUAD#7
V
(7)
V
(7)
Coefficients :
A(1), B(1),..., E(1)
A(2), B(2),..., E(2)
A(7), B(7),..., E(7)
7
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