We should first distinguish between two terms that are often used interchangeably in audio circles but are completely different technologies:
Asynchronous re-clocking or re-sampling: this term describes a pretty simple operation where a digital audio signal is simply re-clocked by a clock from a different time base. There is no interpolation or rate conversion performed on the signal.
Asynchronous Sample Rate Conversion:
This is categorically different, in the sense that SIGNIFICANT interpolation is performed on the Fs_in (input sample rate) signal to minimize error (both time & freq domain) when the ultimate decimation to Fs_out (output sample rate) occurs. Example chips that can perform this function are the CS8420, AD1896 (and their brethren)...
...and the SRC4192 which is the subject of the next project.