CS43L22 DMA constant beep noise
Assuming you are talking about audible noise from the board, not noise in the recreated audio stream, the noise could be caused by modulating the load on the power supply at the frequency of the DMA loop.

Below are some snippets from a good article about diagnosing audio noise from power supplies that explains the effect.


  The most common source of audible noise in a flyback supply is a noisy component. Typically, ceramic capacitors or ferrite transformer cores generate this noise.
  
  Noise in a ceramic capacitor is usually a product of the reverse piezoelectric effect. When a voltage is applied across a dielectric structure, it can induce a mechanical stress or strain that causes the material to deform. As the material deforms, it displaces the air around it and generates noise.
  
  Noise generated by transformer cores, on the other hand, typically is caused by magnetostriction, a process similar to the reverse-piezoelectric effect. That is, many ferromagnetic materials change shape when they’re subjected to a magnetic field. As the magnetic field changes the transformer core, it can cause the core to physically vibrate.