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AN3984 Datasheet(PDF) 5 Page - STMicroelectronics

Part # AN3984
Description  The purpose of this document is to provide a tool to calculate
PDF  46 Pages
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Manufacturer  STMICROELECTRONICS [STMicroelectronics]
Direct Link  http://www.st.com
Logo STMICROELECTRONICS - STMicroelectronics

AN3984 Datasheet(HTML) 5 Page - STMicroelectronics

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AN3984
Overview
Doc ID 022240 Rev 1
5/46
1
Overview
The transfer function for a first-order filter in the digital z-domain is:
Equation 1
For a second-order filter (a biquad) the transfer function is:
Equation 2
This equation can be modified normalizing the a0 coefficient; the new equation is:
Equation 3
The most straightforward implementation form using Equation 3 is:
Equation 4
1
1
0
1
1
0
z
a
a
z
b
b
)
z
(
H
−
−
⋅
+
⋅
+
=
2
2
1
1
0
2
2
1
1
0
)
(
−
−
−
−
⋅
+
⋅
+
⋅
+
⋅
+
=
z
a
z
a
a
z
b
z
b
b
z
H
() ()
()
()
() 2
0
2
1
0
1
2
0
2
1
0
1
0
0
1
)
(
−
−
−
−
⋅
+
⋅
+
⋅
+
⋅
+
=
z
a
a
z
a
a
z
a
b
z
a
b
a
b
z
H
()
()
()
()
()
]
2
n
[
y
a
a
]
1
n
[
y
a
a
]
2
n
[
x
a
b
]
1
n
[
x
a
b
]
n
[
x
a
b
]
n
[
y
0
2
0
1
0
2
0
1
0
0
−
⋅
−
−
⋅
−
−
⋅
+
−
⋅
+
⋅
=



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