Decimation Filter
28-46
Freescale Semiconductor
PXR40 Microcontroller Reference Manual, Rev. 1
Figure 28-22. 1 x 4 Poles IIR Filter Functional Diagram
The generalized difference equation for the IIR filter of
can be written as:
Eqn. 28-1
where
x(n)
is the filter input at time
n, y(n)
is the filter output at time
n
,
N
is the number of feed-forward
filter coefficients minus one,
B
i
are the feed-forward filter coefficients,
M
is the number of feed-back filter
coefficients, and
A
j
are the feedback filter coefficients.
In order to optimize the hardware implementation, the coefficients must be scaled to a maximum range of
+1 to -1. Taking scaling into account,
Eqn. 28-2
All coefficients are scaled down by S, and the output of the accumulator is multiplied by S.
y(n)
Z
-1
Z
-1
Z
-1
Z
-1
+
+
+
+
B
0
Z
-1
Z
-1
Z
-1
Z
-1
+
+
+
+
x(n)
A
4
A
3
A
2
A
1
B
4
B
3
B
2
B
1
x(n-1)
y(n-1)
x(n-2)
x(n-3)
x(n-4)
y(n-2)
y(n-3)
y(n-4)
y n
B
i
x n
i
–
A
j
y n
j
–
j
1
=
M
+
i
0
=
N
=
y n
S
B
i
S
-----
x n
i
–
i
0
=
N
A
j
S
-----
y n
j
–
j
1
=
M
+
=
Summary of Contents for PXR4030
Page 1: ...PXR40 Microcontroller Reference Manual Devices Supported PXR4030 PXR4040 PXR40RM Rev 1 06 2011...
Page 30: ...PXR40 Microcontroller Reference Manual Rev 1 Freescale Semiconductor xxx...
Page 40: ...PXR40 Microcontroller Reference Manual Rev 1 xl Freescale Semiconductor...
Page 66: ...Memory Map PXR40 Microcontroller Reference Manual Rev 1 2 4 Freescale Semiconductor...
Page 120: ...Signal Descriptions 3 54 Freescale Semiconductor PXR40 Microcontroller Reference Manual Rev 1...
Page 860: ...FlexCAN Module 24 50 Freescale Semiconductor PXR40 Microcontroller Reference Manual Rev 1...
Page 1167: ...Decimation Filter Freescale Semiconductor 28 53 PXR40 Microcontroller Reference Manual Rev 1...
Page 1168: ...Decimation Filter 28 54 Freescale Semiconductor PXR40 Microcontroller Reference Manual Rev 1...