User Manual

of IIR filters without their side eects on signal
phase. For example, FIR filters can be used for a
crossover filter instead of common Low Pass and
High Pass IIR filters, reaching very high slopes
without modifies on the phase.
Delay issues of FIR filters
Unfortunately, all that glitters is not gold: there
is a cost to pay also for the use of FIR filters.
The lowest frequency controlled by the filter (its
resolution) is proportional to the length of the
filter in terms of samples and hence to the latency
that introduce in the DSP chain. As shown in the
Table.2, the minimum length of a filter useful for
managing all the audible frequencies introduces a
delay of 21 ms (at 48 kHz of sampling frequency),
delay not acceptable for live performances. The
use of this kind of filters becomes a compromise
between resolution and latency.
Considering the price in terms of latency, FIR
filters can be hence used for correcting a large
part of phase deviations from 0° creating a sort of
Dirac delta (all pass filter): an impulse that doesn’t
aect the amplitude spectrum of the signal but
modifies the phase in order to temporally align
the frequency components of the sound.
Sampling freq. 48 kHz Sampling freq. 96 kHz
Number
of taps
Resolution
(Hz)
Delay (ms)
Resolution
(Hz)
Delay (ms)
32 1500 0.33 3000 0.17
256 188 2.7 375 1.3
1024 47 11 94 5.3
2048 23 21 47 11
4096 12 43 23 21
Table.2 – Delay introduced by FIR filters
The temporal alignment of the frequency
components is clearly visible in terms of Impulse
Response measurements. The phase alignment
increases the dynamic of the signal reproduced
by the loudspeaker, because the energy is
concentrated around the same time and not
distributed as in the case of absence of FIR filter.
The design of the FIR filter for this specific purpose
should start from an accurate measurement of
the loudspeaker phase.
Fig.3 – sum of the FIR filter phase with the loudspeaker phase
FiRPHASE
RCF FiRPHASE processing uses this measurement
and try to invert the loudspeaker’s phase without
touching the amplitude equalization. The heart
of the advanced technique used by FiRPHASE
is a recursive method (Least Squares method)
combined with a proprietary RCF algorithm
that calculates the best FIR filter coecients
set in according to amplitude and phase
constrains. The algorithm corrects phase and
amplitude (if necessary) by taking into account
the weak points of the transducers and the
resonances or cancellations due to the cabinet
of the loudspeaker. This technique permits to the
designers a deep control of phase at mid-low
frequency with relatively small filters, reaching
a higher resolution than that one which theory
suggests.