55.6.2.2 Decimation Filter

The sigma-delta architecture of the PDM microphone implies a filtering and a decimation of the bitstream at the output of the microphone bitstream. The decimation filter decimates the bitstream by either 32 or 64. To perform this operation, a fourth-order sinc filter with an Over-Sampling Ratio (OSR) of 32 or 64 is implemented with the following transfer function:

H (z) = \frac{1}{OS R^{4}} {(\sum_{i = 0}^{OSR - 1} z^{- i})}^{4}

The DC gain of this filter is unity and does not depend on its OSR. However, as it generates a fourth-order zero at Fs/OSR frequency multiples (Fs being the sampling frequency of the microphone), the frequency response of the decimation filter depends on the OSR parameter. See 55.6.2.3 Droop Compensation for frequency plots.

Its non-flat frequency response can be compensated over the 0 to 20 kHz band by using the droop compensation filter when the decimated frequency is set to 48 kHz. See 55.6.2.3 Droop Compensation.

If the decimated sampling rate is modified, the frequency response of this filter is scaled proportionally to the new frequency.

In Figure 55-3 and Figure 55-4, Fs is the sampling rate of the PDM microphone.

Figure 55-3. Spectral mask of an OSR = 32, Fs = 6.144 MHz, Fourth-Order Sinc Filter: Overall Response (continuous line) and 0 to 20 kHz Bandwidth Response (dashed line)

The zeros of this filter are located at multiples of Fs/32

Figure 55-4. Spectral Mask of an OSR = 64, Fs = 3.072 MHz, Fourth-order Sinc Filter: Overall Response (continuous line) and 0 to 20 kHz Bandwidth Response (dashed line)

The zeros of this filter are located at multiples of Fs/64.