A PDM output microphone, such as the ADMP421 or ADMP521 , cannot directly interface to an I 2 S port. Theses microphones should be connected to the PDM input on codecs such as the ADAU1361 and ADAU1761 . The ADMP441 MEMS microphone has an I 2 S output that can be connected directly to a processor or codec's I 2 S input port.
We have an Application Note and a few Circuits from the Lab that explain connections between digital microphones and other devices:
AN-1323: High Performance Digital MEMS Microphone Simple Interface to SigmaDSP Audio Codec
CN0208: High Performance MEMS Digital Microphone's Simple Interface to SigmaDSP Audio Processor (ADMP441, ADAU1446 )
CN0266: High Performance Digital MEMS Microphone Standard Digital Audio Interface to Blackfin DSP (ADMP441, ADSP-BF527 Blackfin)