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AN3984 Datasheet(PDF) 6 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) 6 Page - STMicroelectronics

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Filter stability
AN3984
6/46
Doc ID 022240 Rev 1
2
Filter stability
2.1
Definition
A filter is said to be stable in the z-domain if the roots (or poles) of the filter lie inside the unit
circle.
This definition of stability can be translated in terms of the filter coefficients.
2.2
First-order filter
For a first-order filter, the stability condition that needs to be satisfied is that the pole of the
filter lies within the unit circle.
In terms of the coefficients, the condition can be given as:
Equation 5
2.3
Second-order filter
For a 2nd-order filter, two conditions must be satisfied to ensure filter stability and translated
in terms of the filter coefficients they are:
Equation 6
1
1 <
a
)
1
(
1
2
1
2
a
a
a
+
<
<



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