Measuring Sound: Selecting the FFT Size

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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 room’s 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 don’t 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 room’s 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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