Application Of Fir Filters To Loudspeakers Crossovers; Fir Overview; What Are Iir Filters And Fir Filters; Pros And Cons Of Iir And Fir Filters - Crown DriveCore I-Tech 4x3500 HD Operation Manual

16 Application of FIR Filters to Loudspeaker Crossovers

16.1 FIR Overview

The powerful DSP processing in the latest Crown I-Tech HD Series
amplifiers allow sophisticated Finite Impulse Response filters as well.
FIR filters offer a number of very strong advantages when used to
implement DSP electronic loudspeaker crossovers.
Although high-order IIR filters, which are based on conventional
analog filters, can be designed to provide high stop-band roll-off rates,
the resultant filter phase response is highly nonlinear. This
significantly complicates crossover design and implementation.
As compared to IIR filters, FIR filters can be straightforwardly designed
to allow extremely narrow crossover overlap between adjacent drivers
with high stop-band attenuation and very-high rolloff rates. In-phase
and linear-phase crossovers can easily be designed. Minimizing
overlap dramatically reduces polar lobing and vastly improves off-axis
response through the crossover region.
This white paper briefly describes the characteristics and pros/cons of
FIR and IIR filters, discusses the desirable attributes of FIR filters, and
closes with a set of example measurements on a two-way loudspeaker
system to illustrate the practical application of IIR and FIR crossover
filters. In addition, audio demonstration files are available on Crown's
web site that demonstrates the effects described in this white paper
(see comments at the end of this report).

16.2 What are IIR Filters and FIR Filters?

A filter modifies certain characteristics of a signal such as amplitude/
phase frequency response and wave-shape in a desired manner. This
can be done either in a purely analog manner with a real piece of
hardware such a non-computer based equalizer or filter set, or with a
computer-based instrument running mathematical algorithms using
digital signal processing techniques. These algorithms can be either
implemented in hardware and/or software. The term "digital filter"
refers to the specific hardware or software routine that performs the
filtering algorithm.
page 60
Digital filters may be further classified into two general types: Infinite
Impulse Response (IIR) and Finite Impulse Response (FIR). Fundamen-
tally, IIR filters include feedback (recursion) in their implementation
while FIR filters do not. The feedback in an IIR filter means that the
impulse response of the filter theoretically goes on forever, thus the
"Infinite" term in the name. The impulse response of a FIR filter, on the
other hand, is finite because there is no feedback. Simplified structures
for both these types of filters are shown in Fig. 16.1.
IN
SUM
IN OUT
DELAY
IN DELAY DELAY
DELAY
DELAY
Fig. 16.1 Simplified filter structures of an IIR (top) and FIR
(bottom) filter
The IIR structure on the left feeds back weighted the delayed versions of
the output signal back to the input and thus sets up a form of
recirculation which effectively goes on for forever once a signal is
applied to the input. The FIR structure on the right feeds weighted and
delayed signals to the output ounly and thus can't recirculate the
signals. Effectively there is only a single path through the FIR filter.
SUM
OUT
DELAY
IN DELAY DELAY DELAY
DELAY
DELAY
DELAY DELAY DELAY DELAY
SUM
OUT
I-Tech HD DriveCore Series Power Amplifiers

16.3 Pros and Cons of IIR and FIR Filters

The following table lists several characteristics of the two types of
filters and their pros and cons.
characteristic iiR Filter
Linear Phase
Not Possible
Response
Yes, but with
High Rolloff Rates
phase distortion
Implement
Complex Filters
DELAY DELAY DELAY
Stability Conditionally
Computational
Few CPU cycles
SUM
Complexity
OUT
Common
Implementation
Practice

16.4 Desirable Attributes of FIR Filters

Linear Phase
FIR filters can be designed to have exact linear phase. Linear-phase
filters provide minimal modification to the wave shape of a signal and
also greatly simplify crossover design and implementation because the
filter does not change the phase of the drivers being crossed over.
A linear phase crossover does not mean that the overall response of the
crossover including driver response is linear phase. This can be true
only if the individual drivers themselves are linear phase or can be
equalized to be linear phase.
Electronic crossovers using conventional non-linear phase filters such
as IIR filters can artificially increase the crest factor of a signal and thus
decrease the headroom in the transmission channel.
FiR Filter
Possible
Yes, without
phase distortion
No Yes
Naturally Stable
Massive CPU
cycles
Difficult to
achieve with
limited DSP
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