Filter Design; Low Latency 96 Khz Studio Quality Filters; Measurements Of Two-Way Loudspeaker System - Crown I-Tech 4x3500HD DriveCore Series Operation Manual

16 Application of FIR Filters to Loudspeaker Crossovers

16.10 Filter Design

16.11 Low Latency 96 kHz Studio Quality Filters

IIR filters are typically based on an equivalent analog circuit. Because Because of the extreme computational load imposed by high rolloff FIR
of this, the IIR design process is a straightforward matter of converting crossover filters, a potent DSP and highly optimized FFT Conbolution
an analog filter frequency response specification into digital algorithm are essential to low latency operation at 96 kHz. In-system
coefficients. In contrast, FIR frequency response is usually specified in performance is equally dependent on the filter design process itself.
terms of an ideal, though physically unrealizable filter, e.g. a brick wall I-Tech HD's platform-optimized FFT Convolution algorithm and
lowpass. The FIR filter design is the process of generating coefficients state-of-the-art filter design methodology combine to deliver low
that approximate the response of the ideal filter. The I-Tech HD FIR latency 96 kHz studio quality filters.
filters are designed using a proprietary iterative algorithm using
state-of-the-art signal processing techniques. It yields linear response
and predictable low-noise operation over the entire audio
frequency range.
1600
Required CPU Processing Power
1400
1200
1000
IIR
800
FIR
FFT FIR
600
400
200
0
10 20 30 40 50
Crossover Rolloff Rate - dB/octave
Fig. 16.3 FFT convolution 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.
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I-Tech HD DriveCore Series Power Amplifiers
Real World Benefits
16.12 Measurements of Two-way
Loudspeaker System
The practical advantages of using an FIR-based crossover can be
illustrated by comparing results with an IIR crossover when a two-way
loudspeaker is setup and measured. For measurement purposes, a
small two-way loudspeaker was driven by a Crown I-Tech 12000 HD
power amplifier controlled by Crown's HiQnetTM System ArchitectTM
software. the use of a small system in this application ensures that the
frequency response and angular coverage of the individual drivers has
sufficient overlap through the crossover region to properly illustrate
frequency response and crossover effects.
The following two sets of measurements show the results of using a
conventional IIR filter set up as a 4th-order Linquitz-Riley crossover
and a FIR filter set up as a linear-phase high-rolloff crossover. Each set
of measurements first show the magnitude and phase response of the
crossover alone and then follows the frequency response measure-
ments of the system itself showing individual driver responses, on-axis
responses with the crossover in and out of polarity, and a single
off-axis frequency response where the response exhibits a null due to
driver spacing.
The small two-way system measured here has a woofer and tweeter that
are separated by about 5.5" which creates an off-axis polar null at
about ±25° at the 3 kHz crossover frequency.
60 70 80 90 100
I-Tech HD DriveCore Series Power Amplifiers
16 Application of FIR Filters to Loudspeaker Crossovers
Note that the individual driver responses were first equalized using the
amplifier's parametric equalizer to be more of less flat over a
significantly wide range above and below crossover. After the initial
equalization, the chosen crossover was applied and adjusted. Slight
delay was added to the tweeter channel to compensate for driver offset
to insure that the high- and low- pass sections were in phase
through crossover.
One unexpected benefit of the FIR crossover was the speed up of the
adjustments to insure that the drivers were in-phase through
crossover. This was because the linear/zero phase characteristic of the
FIR filter did not change the phase of the individual drivers when the
crossover was applied! The linear phase characteristic of the FIR-filter
based crossover significantly reduces the setup time of the crossover
as compared to an IIR implementation.
All measurements were accomplished using windowed freefield
techniques in a non-anechoic room at 1m using a 25 ms window. This
window size allows fairly-accurate measurements to be made down to
abut 100 Hz.
IIR Measurements
A 4th-order Linquitz-Riley (LR) crossover with 24 dB/octave slopes at
3 kHz was chosen to demonstrate a typical well-designed conventional
crossover. Although, in conventional terms, a relatively sharp 24 dB/
octave crossover slope is considered quite sharp. The crossover region
spans a relatively wide two octaves. This means that effectively both
woofer and tweeter are radiating simultaneously between roughly 1.5
and 6 kHz.
Operation Manual Operation Manual
The following two graphs in Fig. 16.4 show the theoretical frequency The next two graphs in Fig. 16.5 show the measured individual driver
response magnitude (left) and phase (right) of a 3 kHz LR 4 -order responses of the two-way system driven by the LR crossover as
th
crossover. In each graph, individual curves are shown for the low pass produced by the Crown I-Tech HD amplifier and the resultant summed
(blue) and high pass (red) portions of the crossover. Note that both 1m on-axis response.
low-pass and high-pass filters are 6 dB down and in-phase at the 3 kHz
crossover and thus sum to unity. Note also that the phase of the low-
and high- pass sections is identical but exhibit a 360° phase rotation
10
through crossover. The jump in phase at 3 kHz is a byproduct of the
wrapped phase display, which keeps the phase on a ± 180° scale. The
0
LR responses will sum to unity at all frequencies as expected, but will
exhibit an all-pass non-linear phase characteristic.
-10
10
-20
0
-30
20
Low Pass
-10
High Pass
-20
10
-30
0
20 100 1k 10k 20k
Frequency - Hz
-10
180
-20
90
-30
20
0
Low Pass
-90
High Pass
Fig. 16.5 Measured individual driver responses (left) and overall
-180 summed on-axis response (right) of a two-way system with a 4
20 100 1k 10k 20k
3 kHz LR crossover.
Frequency - Hz
Fig. 16.4 Magnitude (left) and phase (right) of a 3 kHz Linquitz-Riley
4 th -order crossover filter.
Woofer
Tweeter
100 1k 10k 20k
Frequency - Hz
100 1k 10k 20k
Frequency - Hz
th -order
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