Calculating sound pressure level using microphone measurements

I used a microphone to take measurements. I converted the measurements to pressure values (in units of Pascal) using sensitivity value of the microphone. The sampling rate was 8000 samples/sec. I want to calculate Sound Pressure Level (SPL) in terms of decibel, which is with respect to a reference pressure value (Pref = 20 microPascal).

So, I have to calculate

   20*log10(SOMETHING/Pref)

for each octave band.

My question is: How should I calculate SOMETHING in the above expression for each octave band, from the pressure measurements?

Attached is the m-file that I used to calculate SPL value of a cosine function with amplitude 1 and frequency 500 Hz. I implemented 5 different methods to calculate SOMETHING in the above expression which resulted in different SPL values. You can find explanations for each method below. (The file also included A-weighting calculations.) Which one is the correct one or is there another way of properly performing the calculation?

%%METHOD 1 
% 1) take fft -> Y = fft(y)
% 2) calculate db = 20*log10((abs(Y)/Pref))
% 3) For each octave band with fmin=f1 and fmax = f2: 
%   SOMETHING = mean of db in between f1 and f2 
%------------------------------------------
%%METHOD 2
% 1) take fft -> Y = fft(y)
% 2) For each octave band with fmin=f1 and fmax = f2: 
%   2a) zero out Y for other octave bands 
%   2b) calculate RMS using this cutted version of Y.
%       SOMETHING = RMS using this cutted version of Y
%------------------------------------------
%%METHOD 3
% 1) Construct a filter bank
% 2) For each octave band with fmin=f1 and fmax = f2: 
%   2a) apply related filter to the original signal to obtain a signal.
%   2b) calculate rms from the obtained signal.
%       SOMETHING = rms value obtained from the output of filtering
%       operation
%------------------------------------------
%%METHOD 4:
% 1) take PSD. 
% 2) Calculate decibel function using 20*log10(sqrt(PSD)/Pref)
% 3) For each octave band with fmin=f1 and fmax = f2: 
%     SOMETHING = mean of decibel function between f1 and f2
%------------------------------------------
%%METHOD 5:
% 1) take PSD. 
% 2) For each octave band with fmin=f1 and fmax = f2: 
%   2a) zero out other PSD values related to other frequencies
%   2b) calculate the area under PSD
%       SOMETHING = sqrt(area under PSD between f1 and f2)

Answer 1

[Chad Greene]

This is a little bit clunky, but you could bandpass filter your signal for each octave band, then calculate the spl of the bandpass-filtered signal.

Answer 2

[Arnav Mendiratta]

Use the Fractional Octave Band filters .

Answer 3

[Karsten]

Is there a special reason you want to calculate octave bands first? If you just need an A-weighted decibel value for your files...

There is a script to create an A-weighting filter on FileExchange You will need the script adsgn(fs). Insert your sample rate for 'fs'. Now, you can use a simple filter method to perform a-weighting on your files.

Your next step is simply to calculate the rms of the signal and here is your SOMETHING.

[Arnav Mendiratta]

Standard compliant A/C/K weighting filters are also available with Audio System Toolbox:

https://www.mathworks.com/help/audio/examples/audio-weighting-filters.html