User Manual

the magnitude depends only on the gain of the
system.
Multi-way speaker cabinets and traditional IIR
filter-based analog or digital crossovers are
typical examples of non-linear phase systems
with some amount of ‘time smearing’ due to the
all pass nature of the summed electric or acoustic
response.
The goal of a loudspeaker designer is to deliver
a “transparent” sound, where the loudspeaker
is able to reproduce a sound most as possible
close to the original, an important characteristic
for voice-based applications. Any sound
characterization such as equalizations or
distortions should be made by, e.g., the musician
and sound engineer hands, giving them the
freedom to present their own sound to the public.
In classical music applications, the sound can be
perfectly transduced without alterations.
Fig.2 – Visual example of an ideal linear system
The square wave
problem
A 0°-phase loudspeaker delivers to the listener all
the frequencies at the same time, without relative
delays, with the result of a true reconstruction
of the original sound. One of the most relevant
and audible eects in the passage between
“not-0°-phase” and “0°-phase” is the optimal
reconstruction of the transients. Let us think to
a snare, or a picked guitar string: a lot of energy
and frequencies in a very small amount of time.
If the frequencies of the kick or the pick arrive
at the ear not packed but a bit distributed in
time, the impulse loses energy, dynamic, detail.
This could be understood by using a squared
wave that is the sum of a fundamental sin wave
and a number of its odd harmonic at higher
frequencies. If the harmonics are delayed respect
to the fundamental, the reconstruction fails.
Original squared
wave signal at the
loudspeaker input.
(a)
Squared wave signal
reconstructed by the
loudspeaker with
harmonics out of
phase.
(b)
Squared wave signal
reconstructed by the
loudspeaker with
harmonics in phase.
Table.1 – Visual example of a square wave reconstruction from (a) a phase-distorted
system and (b) a phase-coherent system
The loudspeaker is not only made of transducers
but crossover and equalization filters act a
fundamental role in the final result. Analog filters
or digital IIR filters produce phase distortions
around the frequency on which they act
adding them to the ones already present in the
transducers.
FIR filters for phase
linearization
The modern DSPs permit a pre-compensation
of these phase distortions in order to deliver a
0°-phase signal. The most useful and powerful
way is the use of FIR filters (Finite Impulse
Response filters). A FIR filter is nothing but a
set of coecients, representable as an impulse
response (IR) in the time domain. The digital
audio signal is filtered, hence modified, with
the FIR by mean a mathematic operation called
“convolution”.
This kind of filters introduces a delay, the time
necessary to the signal for passing all the length
of the filter. Luckily, the time delay is equal for
all the frequencies (no relatives delays between
frequencies): in this particular case, they are
named linear phase. A linear phase FIR filter can
manipulate the amplitude equalization of a signal
without distorting its phase, it can act as a bank
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