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Measuring Sound: Selecting the FFT Size
By Sam Berkow
& Pat Brown
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A Movie Example
The required frame rate for film recording is 30 frames- per-second.
This is the required frame rate to make a series of static pictures
to appear like fluid motion to an observer. If a lower frame rate
were chosen, the motion might look jerky, especially
with fast movement by the subject. Using 30 frames-per-second as
a reference, we could describe the length of a movie in frames,
which would simply be 30 times the number of seconds of the movie.
The duration of a one hour movie would be
60 seconds x 60 minutes x 30 frames = 108,000 frames
If you wanted to record a two-hour event using a movie camera at
this rate, you would need a tape long enough to hold 216,000 frames.
As you can see, frame count and duration time could be two different
ways to describe the length of a movie.
In our movie example, 30 frames were collected each second to provide
sufficient data to convince the human senses that continuous motion
was taking place.

Back To Audio
In sampling audio events, the required sampling rate to do the
same is twice the highest frequency that you wish to observe. If
this is extended to the arguable limits of human perception, a sampling
rate of at least 40 kHz would be required to accurately characterize
a 20 kHz waveform. Our industry uses 44.1 kHz and 48 kHz for full
bandwidth audio, and lower sampling rates when less bandwidth is
acceptable.
The required FFT size becomes the sampling rate times the duration
of the rooms decay in seconds. As such, at a 48 kHz sampling
rate, a 1 second room decay would require 48 K samples to record.
A two second room would require twice this amount, and so on. As
with the video example, you need to make certain that you are sampling
long enough to capture the whole event.
Another trade-off that we can make when recording video is the
tape speed. If the tape is slowed down, it will last longer. Of
course, you dont get something for nothing, so there is a
reduction of quality in the recording. Audio measurements work the
same way, in that if you need a longer FFT size than you can acquire
using 48K sampling, you can reduce the sampling rate. The trade-off
here is that you will now be unable to record any frequency higher
than half the sampling rate. This sacrifice is perfectly acceptable
in many applications.
The chart below shows some examples of FFT sizes and their resultant
time spans.
Selecting the FFT Size...

In acoustical measurements, required PET size is determined by the
time that it takes for the sound to completely decay in the room.
It can be found by multiplying the sampling rate by the length of
the rooms decay. This will also determine the frequency resolution
of the measurement, since one must measure a long enough time span
to capture 1 cycle of the lowest frequency of interest. Sampling
for 1 second at 44 K samples/sec would yield 44 K data points and
1 Hz frequency resolution.
1 * 44k = 44 K samples
44k/44k= 1Hz resolution

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