My problem now is, that I want to convert that file into an audio format (.wav) so I can analyse and filter it with MATLAB or Audacity or any audio software that will work.
Audacity can import "raw" uncompressed audio data files but you have to type-in all of the information it normally gets from the file header such as the bit depth, sample rate, number of channels, etc. Then, you can optionally export to WAV (or other standard audio format).
I'm sure MATLAB can do that too, since MATLAB isn't strictly an audio program, but it may be more work for you to re-format the raw bytes into audio samples (if it's not simple 8-bit audio).
* Since the Arduino ADC can't read negative values, the input is biased giving you biased A(unsigned) data. For signed formats, you'll have to subtract-out the bias before writing the WAV file. And of course, you'll need to scale the ADC data (12-bits form the Due) up or down to 8 or 16 bits for a standard audio file.
but my aim is to get real time audio and analyse/filter it on the fly. Is it possible to transmit the audio over USB?