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Measurement Duration - FFT Size
The last parameter of interest in sampling data is the duration
of the signal required for the measurements. This sets the storage
requirement for the samples, just as with film recording the number
of film frames available will determine the total length of a movie.
As with film re cording, the number of samples must be sufficient
to capture the event of interest, and for acoustical measurements
this is usually (but not necessarily) the full decay time of the
room being measured. Most systems refer to this as FFT size or length,
and the values required for acoustics will range from about 16,000
samples (about 1/3 second at frill bandwidth) and up. Shorter FFTs
are sufficient for shorter duration events, such as measuring direct
field responses only (of interest to loudspeaker designers). Longer
FFTs are required for rooms with very long de cay times.
To review, gathering data with acoustic analyzers requires that
the user select an appropriate
- Sampling Rate (time resolution)
- Quantization (amplitude resolution)
- FFT Length (Time duration of measurement)
"Appropriate" in the above means that the user must make
a judgment as to the nature of the event being recorded, and select
the parameters accordingly. For example, if we wished to perform
an acoustical evaluation of a room whose decay time is 1 .5 seconds,
we might select:
- Sample Rate = 44.1 kHz - This would allow ac curate data to
be recorded for the full audible passband
- Quantization = 16 bits - Though not user select able on most
systems (this is a commonly used resolution) this provides a "CD
quality" record of the event.
- FFT Length = 65,535 points - This will allow the 44.1 kHz sample
rate to be maintained for the full decay time of the room (1.5*
44,100).
Again, these setup parameters are common to most every available
measurement system, but each system will have a unique way of selecting
the parameters. Read the manual specific to the system that you
are using.
Types of Analyzers
As stated earlier, traditional measurement methods allowed for
the continuous viewing of the sound level at one point that results
from a signal with a flat spectrum being fed to the system under
test. The information being observed on the analyzer is not the
characteristic of the loudspeaker alone, but a composite of the
signal processing chain, the loudspeaker response and the room response.
To determine the characteristic of the loudspeaker an investigator
would have to place the loudspeaker in an echo-free (anechoic) environment
and ensure that the signal into the loudspeaker has a flat (or known)
spectrum.
One major benefit of modern analyzers is that they allow the effect
of each part of the system to be independently characterized. This
is accomplished by dividing the raw output of the device-under-test
(DUT) by the in put (or, equivalently, subtracting their dB levels).
The resulting data is called a transfer function and provides
a description of how the DUT has changed the signal. This and a
second, fundamentally different way, of obtaining the transfer function
of sound systems are described next.
1. Dual-channel FFT - This type of analysis actually
requires that two measurements to be made. A broad band stimulus
is input to the system, and both the stimulus and the response of
the system are digitally sampled and stored in computer memory,
where they are com pared and the difference displayed. This is the
transfer function of the DUT. Dual-channel FFT's have the ad vantage
of allowing any broadband stimulus to be used, including music,
however accuracy could suffer if the music does not have significant
energy in all frequency bands.
2. Maximum-Length Sequence (MLS) - This method
uses as a stimulus a noise excitation (a random- like binary string
of one's and zero's). It is random within the length of the digital
delay line used in its generation, but it then repeats. This is
input to the device under test and stored in the computer's memory.
The response of the DUT is acquired and compared to the input string,
yielding the transfer function of the DUT. MLS analyzers have the
advantage of very good signal-to-noise characteristics, allowing
accurate data collection under noisy conditions.
3. Time-Delay Spectrometry (TDS) - TDS uses a
sinusoidal signal whose frequency sweeps linearly over the frequency
range of interest as the input to the DUT. The signal out of the
DUT is mixed with the outgoing signal, yielding a set of sinusoidal
signals of frequencies determined by their delay times. A filter
selects the signal of interest (usually the direct path signal and
there fore the one having the lowest frequency). Subsequent processing
yields the frequency response of the system, which can be further
processed to yield the impulse response of the system.
Any of these methods can be used to measure the transfer function
of a system or any part of a system, and each method has a unique
set of advantages and disadvantages. The following assumes that
a system appropriate to the immediate need has been selected and
discusses what the acquired data can tell us about an installed
sound system.
Figure 1. Impulse Response
The Transfer Function
We have described several methods for determining the impulse response
of a system. We often obtain a crude impulse response by making
a "hand clap" to produce a fairly sharp sound, and listening
to the echoes. Figure 1 shows what the response to a very sharp
impulse might be.
The "hand clap" approach to impulse response testing
has some severe shortcomings with regard to signal-to-noise ratio
and distortion. Modern analyzers use alternative methods to determine
the impulse response of a system, almost none of which involve the
use of an impulse! Whichever method is used, when we know the impulse
response of a system, we know its transfer function. In other words,
if we know how that a system responds to an impulse, we can determine
how it will respond to any stimulus.
Figure 2. Doublet Response
All of the measurement methods described use stimuli that are spread
out over time. The impulse response results from post processing
of the acquired data. As a result, the correlation between the sound
the analyzer makes and the data displayed on the screen will be
very subtle. This is one of the most confusing aspects of all of
these systems.
There are many possible ways to process and view the impulse response.
Figure 1 shows a "raw" impulse response. Figure 2 shows
the "doublet" of the impulse response, which is obtained
by phase shifting the Fourier components of the impulse response
by 90 degrees. This "imaginary" impulse is used with the
impulse in obtaining the Energy-Time Curve (ETC). Figure 3 shows
the impulse response displayed on a dB (log) scale. Figure 4 shows
an ETC. All of these are alternate views of the same set of data
points. While the "raw" impulse response most closely
depicts what is happening physically (sound pressure as a function
of time) the "post processed" plots can help correlate
the information better with what we hear.
Figure 3. Log-Squared Response
Figure 4. Energy-Time Curve
Part two of this series will look at more ways to process the impulse
response to reveal useful information about the system under test.
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