dsp56800 Freescale Semiconductor, Inc, dsp56800 Datasheet - Page 404

• Manufacturer Part Number: dsp56800
• Description: 16-bit Digital Signal Controllers
• Manufacturer: Freescale Semiconductor, Inc

B.1.5
Many digital-filter design packages generate coefficients for Direct Form II infinite impulse response (IIR)
filters. Often, these coefficients are greater in magnitude than 1.0. This implementation is suitable for IIR
filters with coefficients greater in magnitude than 1.0 because it allows the user to simply divide all
coefficients generated by 2. The general form of the IIR filter’s output y(n) at time n, a linear combination
of the present input, the M previous inputs and the N previous outputs, is given by:
The Biquad Direct Form II realization of the IIR filter above can be described in the following two
equations:
B-8
; Biquad: M=N=2
; w(k)/2 = x(k)/2 + (a1/2) * w(k-1) + (a2/2) * w(k-2)
; y(k)/2 = w(k)/2 + (b1/2) * w(k-1) + (b2/2) * w(k-2)
; D High Memory Order - w(k-2)1,w(k-1)1,w(k-2)2,w(k-1)2,...
; D Low
w k ( )
y k ( )
N Cascaded Real Biquad IIR Filters (Direct Form II)
opt
MOVE #W_Vec5,R0
MOVE #C_Vec5,R3
MOVE #N_Biquads,LC
MOVE #-1,N
MOVE
ASR
MOVE
DO
MAC
MAC
ASL
ASR
MAC
MAC
Memory Order - (a2/2)1,(a1/2)1,(b2/2)1,(b1/2)1,(a2/2)2,...
=
=
n
m
∑
∑
N
=
M
=
cc
A
LC,EndDO1_5
Y0,X0,A
Y1,X0,A
A
A
Y0,X0,A
Y1,X0,A
1
0
a
b
n
m
⋅
w k n
⋅
w k m
(
(normalizing by b0). This version uses two pointers.
(
–
y k ( )
–
)
X:InputValue,A
X:(R0)+,Y0
X:(R0)+N,Y1
Y1,X:(R0)+
A,X:(R0)+
X:(R0)+,Y0
+
=
)
x k ( )
=
n
∑
DSP56800 Family Manual
N
=
b
1
0
a
=
⋅
n
w k ( )
y k n
a
(
1
⋅
–
w k 1
X:(R3)+,X0
X:(R3)+,X0
X:(R3)+,X0
X:(R3)+,X0
X:(R3)+,X0
+
(
)
b
1
+
–
⋅
m
w k 1
∑
M
)
=
(
+
0
b
a
–
m
2
; 2
; 2
; 2
; 1
; 1
; 1
; 1
; 2
; 1
; 1
; 1
; 1
; 1
; 1
x k m
⋅
)
(
w k 2
+
(
–
b
2
–
2
2
2
1
1
1
1
3
1
1
1
1
1
1
⋅
)
w k 2
)
(
+
x k ( ) for N=2
–
ptr to w(k-2),
ptr to a2 coeff
number of biquads
allow traverse prev
input fr peripheral
X0=.5a2
Y0=w(k-2)
start casc biquads
Y1=w(k-1) X0=.5a1
store interm result
X0=.5b2
X0=.5b1
A=.5Y(k) for biquad
Freescale Semiconductor
) for M=2