Implementing IIR/FIR Filters

“In the directform
implementation,
the a i and b i are
used directly in
the difference
equation, which
can be easily
programmed on
a high-speed
DSP such as the
DSP56001.”
SECTION 2
Second-Order
Direct-Form IIR
Digital Filter Sections
The traditional approach to deriving the digital filter
coefficients has been to start with the digital z-domain
description, transform to the analog s-domain to understand
how to design filters, then transform back to
the digital domain to implement the filter. This approach
is not used in this report. Instead, formulas are
developed relating the s-domain filter to the z-domain
filter so transformations to and from one domain to the
other are no longer necessary.
The Laplace or s-transform in the analog domain was
developed to facilitate the analysis of continuous time
signals and systems. For example, using Laplace
transforms the concepts of poles and zeros, making
system analysis much faster and more systematic.
The Laplace transform of a continuous time signal is:
Xs ( ) = L{ x() t }
xt ()e st –
∞
dt
Eqn. 2-3
where: L = the Laplace transform operator and
implies the operation described in Eqn. 2-3
MOTOROLA 2-1
∫
0