Curious noise on FPGA Microcontroller connection
This has to be a protocol error between FPGA and MCU. Your low-level AC signal (audio) from the FPGA is being mis-read (somehow) by the MCU. The noise looks like incorrect value of the sign bit appearing as large impulses on the decoded signal.

As Dave Tweed says, you don't want the MCU to be reading the signal while the FPGA is updating it. Are you reading all the GPIO pins with a single instruction? I'm guessing not.

You might want to bombproof this transfer with a handshake from FPGA to MCU. Update the audio sample then assert a Req signal. Wait for the MCU to assert an Ack signal, retract Req, then wait until MCU retracts Ack (and the next sample is ready) before updating the signal again. 

In the MCU, only access the audio data when Ack is 1.