Implementing IIR/FIR Filters

Eqn. 2-18 can be directly implemented in software,
where x(n) is the sample input and y(n) is the corresponding
filtered digital output. When the filter
output is calculated using Eqn. 2-18, y(n) is calculated
using the direct-form implementation of the
digital filter.
There are other implementations which can be
used for the same system (filter) transfer function,
H(z). The canonic-form implementation and the
transpose-form implementation are discussed in
subsequent sections. First, the directform implementation
will be applied to the transfer function,
H(s), developed in SECTION 1 Introduction.
2.6 Digital Lowpass Filter
Using the analog transfer function, H(s), from Figure
1-1, Eqn. 2-13 and Eqn. 2-14, the digital transfer
function, H(z), becomes that shown in Figure 2-10,
where the coefficients α, β, and γ are expressed in
terms of the digital cutoff frequency, θ c , and the
damping factor, d. The value of the transfer function
at θ = θ c in the digital domain is identical to the value
of the s-domain transfer function at Ω= Ω c :
H
z
e jθc
( ) =
H
s
( jΩ
c
)
Eqn. 2-19
As shown in Figure 2-11, the digital gain and
phase response calculated from the equations of
MOTOROLA 2-9