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Bilinear Transformation
The bilinear transformation may be defined by
where
is an arbitrary positive constant that we may set to map one
analog frequency precisely to one digital frequency. In the case of a
lowpass or highpass filter,
is typically used to set the
cut-off frequency to be identical in the analog and digital
cases. The bilinear tranform was introduced in 1947 for discrete-time
filter analysis (a year after the first general-purpose computer--the
ENIAC--was announced) by Arnold Tustin,I.2 so it is also called ``Tustin's Method.''
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