Time domain to frequency domain conversion of audio signals to extract 1/3 octave frequencies
As per my knowledge it is desired to convert received signals from time domain to frequency domain and extract the noise levels for each 1/3 octave frequency band.


No. This is needlessly complicated. A-weighting and C-weighting can be implemented through simple FIR or IIR filtering directly in the time domain. There are public domain filter designs avialble. For example check out https://www.mathworks.com/matlabcentral/fileexchange/69-octave


  It displays noise levels in Leq sound pressure levels.


Your biggest problem will be to deal with microphone calibration. Both frequency response and overall sensitivity of Android microphones are all over the place and vary a great deal from model to model, can change between Android version and sometimes are actually actively modified by each carrier. Without some sort of calibration, you can display a number but it won't be Leq and it will mostly be meaningless.

iOS might be easier: Apple does a much better job in controlling microphone consistency in design and supply chain. For a meaningful Leq estimate you still need calibration, but it's going to be less severe and there is a much smaller number of models/iOS versions to deal with.