Calculate Third Octave Band Response from Narrowband Data

[jasonbot]

I have a signal that I am able to calculate through an acoustic model for airfoil noise. I am told that the model solves for a narrowband frequency response, however, my measurement data is provided in third-octave band representation.

How do I convert my current dataset to the third octave?

L_p(ƒ)=20log(P(ƒ)/P₀)

 

[nbryan5]

The most common way to convert a narrowband frequency response to third octave is by using the A-weighted filter. This filter takes the power spectrum of the signal and applies a frequency-dependent weighting factor to each frequency bin, which is then summed together to calculate the third-octave band levels. The formula for the A-weighted filter is given by: Lp(ƒ)=20log(P(ƒ)/P0), where P(ƒ) is the power spectrum of the signal and P0 is a reference value. To obtain the third-octave band levels, you will need to calculate the A-weighted filter at each third-octave band center frequency and then sum the results.