Intel 2920 Design Handbook page 58

SUMMARY OF FILTER CHARACTERISTICS
5.5.1 II R Filters
The traditional approach to the design of IIR digital
filters involves transforming an analog filter into a
digital filter that meets prescribed specifications. This is
a reasonable approach because
1) The art of analog filter design is highly advanced.
Since useful results can be achieved, established
analog design procedures present advantages.
2) Many useful analog design methods have relatively
simple closed-form design formulas, greatly
facilitating the implementation of the correspond-
ing digital filters.
3) In many applications it is of interest to use a digital
filter to simulate the performance of an analog
linear time-invariant filter.
The conversion of an anlog filter into a digital filter is
accomplished in a number of ways: impulse invariance,
direct transformation using s- to z-plane transforms,
conversion of differential equations to difference equa-
tions, and direct synthesis techniques. Some of these are
discussed in the next section. In each approach, known
analog filter characteristics in the frequency domain are
converted to similar characteristics in the z-plane of the
digital filter. Table 5-2 lists some of the direct
transforms which are used.
Table 5-2. Direct Transforms
Matched Z
Left Integration
Trapezoidal
Bilinear
Prewarped Bilinear
Each of these techniques introduces a nonlinearity into
the resulting amplitude and phase characteristics of the
original analog filter. Phase equalizers may be designed
to linearize the phase characteristic of the transformed
digital filter.
5.5.2 FIR Digital Filters
Finite impulse response filters offer several advantages.
Some of these advantages are:
1) FIR filters can be designed to have exactly linear
phase. Linear phase filters are important for
applications such as speech processing and data
transmission, where phase distortion is harmful.
5-7
·--------.,0
t
62
Figure 5-7. Digital Filter Module
(Second Order Section)
2) FIR filters which are realized using a non-
recursive structure are always stable.
3) Roundoff noise, inherent in any realization using
finite precision arithmetic, can easily be made
small for the non-recursive FIR filters.
4) Adaptive filters are more easily relayed using
FIR techniques.
One disadvantage of FIR filters is that a large number
of delay elements are needed to obtain a sharp cutoff,
thereby requiring a large amount of processing. Thus a
limited resource like the 2920 signal processor can
achieve more filter complexity using IIR approaches.
The characteristic of interest is the ideally linear phase
which can be achieved with the FIR filter. The desired
amplitude characteristic can be achieved with arbitrary
accuracy by increasing the degree of the filter without
affecting the phase.
5.5.3 Canonical Forms Of Digital Filters
Figure 5-7 is a block diagram of a digital filter module.
Each block labeled z-I is a unit delay, i.e., a delay of
one inter-sample interval. The other blocks are
multipliers (X) and adders (L). The values AO, AI, A2,
B 1, and B2 are coefficients which determine the
behavior of the module.