| Understanding
Sound System/Room Interactions
by Sam Berkow
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As an alternate approach to trying to find a measurement that
correlates with what we hear, we can try using a longer time window
to “see” the LF response with better resolution. A longer
time window of approximately 250 msec is shown in Figure #4.
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Figure #4: The impulse response
of a 1250 seat multipurpose hall. The vertical lines suggest
a time window that INCLUDES most of the effects of the room.
The time window shown is approximately 0.25 seconds.
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To transform this longer “slice” of the impulse response
into the frequency domain, we will use an 8k FFT which represents
8K/48000 seconds or 0.171 seconds. Notice again that this time window
includes both the direct sound and the response of the room.
In Figure #5 the low frequency information is seen in adequate
resolution, however the high frequency results look confusing. The
plot shows data that has 5 Hz resolution (i.e. one data point every
5 Hertz). While this resolution provides excellent LF resolution
(between 31 Hz and 62.5 Hz there are 15 data points. However at
HF we have excessive resolution - between 4kHz and 8kHz there are
approximately 800 data points. Simply stated, the longer time window
provides good LF resolution, but excessive HF resolution.
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Figure #5: The frequency
response of the direct sound portion of an impulse response
of a 1250 seat multi-purpose hall. The response was calculated
using a 8192 point FFT (which equals a 8192/48000 or ~107
msec). As you can see the frequency response shows low frequency
energy that is much more pronounced than seen with the shorter
time window.
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The result of studying these plots might lead you to conclude that
in order to make measurements that correlate well with our listening
experience, we must use very short time windows that isolate the
direct sound at high frequencies, and increasingly longer time windows
as we look at lower frequencies. At first glance this idea might
seem to violate the often quoted phrase, “One can only affect
the direct sound with processing.” However this is not the
case. At mid-low and low frequencies, the interaction of a sound
system and a room can be affected and optimized by signal processing.
In other words, at low frequencies (long wavelengths) the direct
sound and reflections from nearby surfaces combine to form a composite
response. It is this composite response that a listener hears.
The ability to measure several time windows simultaneously provides
a measurement that both correlates well with human hearing and provides
insight into how the signal being sent to the loudspeaker can be
tailored (via equalizers, or other processing) to optimize the loudspeaker/room
interaction.
Our last figure shows a measurement of a loudspeaker system that
includes multiple time windows and displays both the magnitude and
phase response of the “system.”
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Figure #6: This frequency
response was calculated using a multi-windows transfer function.
One result of this is the trace has equal resolution (24 data
points) in each octave from 20 Hz to 20 kHz, and is therefore
call a Fixed-Point-Per-Octave or FPPO transfer function. Both
magnitude and phase traces are shown.
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Conclusion: The use of multiple time windows allows one
to isolate the direct sound of a loudspeaker in a real-world situation
at high frequencies. However at lower frequencies longer time windows
that include the loudspeaker/ room interaction have been found to
correlate well with our listening experience. The use of multiple
time windows in a single measurement is an extremely interesting
way to measure and optimize the response of a sound system in a
room.
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