One of the traditional limitations of PET based analysis was the way the frequency domain data points were distributed linearly across the audio spectrum. In the case of a 44100 sampling rate and 4096 point PET, we have 2048 frequency domain points, spaced every 10.8 Hertz. This means that in the octave between 31.5 Hz and 63 Hz there are only 3 data points, while between 4000 Hz and 8000 Hz there are about 400 data points. The problem is that humans hear logarithmically in frequency. Notice that the perceived change in pitch from 31 to 63 is 31 Hz wide and represents one octave, while the change from 4000 Hz to 8000 Hz is also one octave wide but 4000 Hz wide! This is in contrast to the linear spacing of the frequency domain data from a standard FFT.

To resolve this issue, it is possible to use a mathematical technique called the Chirp-Z transform. The output of the Chirp-Z provides data points which are logarithmically spaced in frequency. The problem is that the Chirp-Z is very complicated to do and requires more computer power than is readily available. The answer to this is the use of multiple FFTs at different sampling rates and sizes which can be put together to provide an equal number of frequency domain data points in each octave across the audio spectrum. Currently systems which provide 24 and 16 points per octave transfer functions are available. An interesting feature of these fixed-point-per-octave FFTs is that the use of several FFTs with different sampling rates and EFT sizes provides longer time constants at lower frequencies and shorter time constants at higher frequencies… which correlates extremely well with the nature of human hearing. pb/sb

The graph above shows a frequency response curve obtained using a standard 4096 point FFT. note the ”grassiness“ in the high frequency response due to the large number of FFT points and subsequent high resolution.

Measured data of the same loudspeaker but this time using the "Fixed point per Octave" function of JBL-Smaart. The high frequency data ismuch smoother. many resarchers feel that the human ear/brain system works in a similar manner.