Operation Manual
I-Tech HD DriveCore Series Power Amplifiers
page 60
I-Tech HD DriveCore Series Power Amplifiers
Operation Manual
page 61
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.
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.
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.
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.
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.
Characteristic
IIR Filter
FIR Filter
Linear Phase
Response
Not Possible
Possible
High Rolloff Rates
Yes, but with
phase distortion
Yes, without
phase distortion
Implement
Complex Filters
No
Yes
Stability
Conditionally
Naturally Stable
Computational
Complexity
Few CPU cycles
Massive CPU
cycles
Implementation
Common
Practice
Difficult to
achieve with
limited DSP
DELAY
DELAY
DELAY
DELAY
DELAY
DELAY
DELAY
IN
IN
DELAY
DELAY
SUM
SUM
OUT
OUT
DELAY
DELAY
DELAY
DELAY
DELAY
DELAY
DELAY
IN
IN
DELAY
DELAY
SUM
SUM
OUT
OUT
16.7 Polar Lobing Error
Polar lobing is a potential problem when spatially separated
non-coincident drivers are crossed over. Throug the crossover region
both drivers are radiating simultaneously. This may cause a narrowing
of the coverage pattern and the creation of a directional lobe. It is very
desirable that this lobe face straight ahead, and not directionally
wander with frequency. If it does, lobing error occurs.
Polar lobing error is minimized when the low- and high-pass sections
of the crossover are in-phase with each other throughout the crossover
are in-phase with each other throughout the crossover region. This is
an attribute of the “Linquitz-Riley” (LR) type of crossover rewponses.
Polar lobing can also be minimized by reducing the crossover overlap
with zero-phase sharp-cutoff filters such as provided by FIR filters.
16.8 Crown’s Implementation of FIR Filters
Crown’s FIR filter implementation uses state-of-the-art digital signal
processing techniques which are highly optimized for the DSP engine
in the I-Tech HD series of amplifiers.
16.9 FFT Convolution
The resource requirements of a high-performance FIR filter in terms of
cpu cycles per sample, datapath bandwidth and memory footprint can
exceed those of an IIR solution by several orders of magnitude. Key to
an efficient FIR implementation is the use of Fast Fourier Transform
(FFT) techniques to accelerate the FIR convolution process, which is
usually thought of as a time domain operation. Time domain
convolution is something to be avoided, because it is extremely
expensive in the computational sense. Fortunately, signal processing
theory tells us that multiplication in the frequency domain is equivalent
of convolution in the time domain. This is important because
multiplication is very efficient in comparison to convolution. Of course,
an efficient and speedy means of moving between the time and
frequency domains is also required. This is where the FFT comes in.
Using the FFT to transform back and forth between the time and
frequency domains so as to replace convolution with multiplication is
referred to as FFT Convolution. Figure 16.2 shows a block diagram of
the FFT convolution process.
Fig. 16.2 FFT conbolution block diagram. here the input and filter
impulse responses are both individually FFT’d and multiplied and then
inverse FFT’d to genterate the output.
16 Application of FIR Filters to Loudspeaker Crossovers
16.5 High Rolloff and Steep Slopes
FIR filters can be designed to have extremely high stop-band rolloffs
and exceptionally steep slopes which greatly minimizes crossover
driver overlap. In a conventional analog or analog-based IIR
crossover, driver overlap can extend over two or three octaves. FIR
crossovers dramatically restrict the operating overlap bandwidth of the
crossover which considerable reducers the range over which both
upper and lower range drivers are radiating in the same frequency
range. Very narrow overlaps of one-third octave or less can be
implemented with FIR filters.
In addition, the extremely steep slopes of FIR filters offer greater driver
protection and reduced distortion. Beyond the driver’s linear frequency
range, energy is attenuated so rapidly that most non-linearity’s cease to
be a problem. The driver does not need to be as well behaved outsied
its frequency range. Power handling capability of HF drivers is much
improved. The narrower crossover region also lessens the need for
precise driver time alignment since the overlap region is so small.
16.6 Stop-band Attenuation
Associated with the very high stop-band rolloff of an FIR filter, is the
associated extremely high stop-band attenuation. This minimizes
interaction between adjacent drivers such as a low-frequency woofer
signal bleeding into a tweeter and thus causing intermodulation
distortion. In a home theater setup, high stop-band attenuation of the
subwoofer minimizes subjective localization of the woofers due to
hight-frequency bleed through.
input
output
filter impulse response
FFT
FFT
X
inv FFT
