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Octave Scaling

Octave band analysis has been defined as a standard for acoustic analysis. This type of spectrum is called constant percentage band (CPB) because each frequency band is a constant percentage of its center frequency. In other words, the analysis bands become wider in proportion to their center frequencies.   1/1 and 1/3 octave spectra are the most frequently used formats in acoustical measurements - three 1/3 octave bands encompass one octave.

It can be argued that the frequency resolution in octave band analysis is too poor to be of much use, but a major advantage of constant percentage band analysis is that a very wide frequency range can be displayed on a single graph and the frequency resolution at the lower frequencies can still be fairly narrow.  The naturally occurring ambient spectra will be found to slope downwards at the highest frequencies, and a constant percentage band (CPB) spectrum of the same data will usually be more uniform in level over a broad frequency range.  Pink noise slopes downward at 3dB per octave and produces a perfectly flat octave spectrum.  

Standard octave band center frequencies and bandwidths have been agreed upon by the international community.  These standards are used by  SpectraPLUS-SC.

Most octave analyzers are analog instruments and use analog filters for each band.  SpectraPLUS-SC is a digital analyzer and utilizes the FFT algorithm to compute the narrowband (linear) frequency spectrum.  This linear frequency spectrum is then apportioned among the octave bands to produce the corresponding octave spectrum.  

As you would expect, the FFT size directly determines the number of octave bands that can be computed.  At the low frequencies, there are only a small number of narrowband bins which fall within the corresponding octave band limits.  The number of 1/3 Octave bands produced for various FFT sizes are listed below:

FFT size   Number of 1/3 Octave bands
     32                             3  
     64                             6
     128                           10
     256                           13
     512                           16
    1024                          19
    2048                          22
    4096                          25
    8192                          28  
    16384                        31
   32768                         34
   65536                         36 


The actual band frequencies are determined by the sampling rate and decimation ratio. 


See also:  Scaling, FFT size