Perform summation on a cell array according to a equation

Hello, I am required to calculate the overall sound power which is the result of adding the columns(element wise) of a cell array. The addition must be performed according to the equation as can be seen in the attached figure 'Formula.png'. I am also attaching the 'Myvariables.mat' file which contains the cell array.

The 'L1' and 'L2' in the figure in my case represents the elements of cell array(column-wise). Please help!

Thank you in advance!

[Stephen23]

Continuation of this question:

http://www.mathworks.com/matlabcentral/answers/251779-logarithmic-summation-of-cell-array

Answer 1

[Geoff Hayes]

Karthik - if we assume that all elements in your array are in units of decibels (which you have stated in your previous questions at http://www.mathworks.com/matlabcentral/answers/251779-logarithmic-summation-of-cell-array), then the above equation is telling us that we have to invert those values, sum them, and then apply the 10*log10 to this sum. We can do this as follows with a sample array

 b = 122; % random values created in the range of 100 and 122 decibels
 a = 100;
 dbValues = (b-a).*rand(100,1) + a;

 overallSoundDb = 10*log10(sum(10.^(dbValues/10)));

As an aside, if y is in decibels and is calculated as

 y = 10*log10(x)

then to get the inverse of y (i.e. x) we do

 x = 10^(y/10);