Deltasigma ADCs in a nutshell, part 3: the digital/decimator filter
Following the modulator in the deltasigma ADC is a digital/decimator circuit. This circuit samples and filters the modulator stream of 1bit codes. At the modulator output, highfrequency noise and highspeed sample rates are problems. However, because the signal now resides in the digital domain, you can apply a digitalfilter function to attenuate the noise and a decimator function to slow the output data rate. Designers often intertwine the digital filter and decimator functions in the same silicon.
Figure 1 shows the signal as it travels through the digital/decimatorfilter functions. The digitalfilter function operates at the same rate as the modulator sampling rate (Figure 1a). Notice that the 24bit codetrain resembles the original signal (reference 1 and reference 2). In the time domain, it looks like the digitalfilter function is responsible for the low noise and high resolution of the deltasigma converter. However, this function provides a secondorder impact on the system noise by rejecting higher frequency noise, where the noise shaping from the modulator dominates noise reduction in the lower frequency band (Figure 1b).

The digitalfilter function provides a digital version of the input, but the data rate is still too fast to be useful. Although it might appear that you have an abundance of highquality, multibit samples at a high sampling rate, you don’t need most of this data.
The second function of the digital/decimator filter is the decimator. Decimation is the process of reducing a digital signal’s output rate to the system’s Nyquist frequency. One simple way to implement a decimating function is to average together groups of 24bit codes (Figure 1c). The decimator accumulates these highresolution data words, averages several words together, outputs the average results, and dumps the data for the next average. A more economical way to implement a lowpower decimator function is to simply pick out a 24bit word every Kth sample without performing additional averaging. (K is equal to the oversampling or decimation ratio.)
Almost all deltasigma converters incorporate a class of averaging filters called sinc or FIR filters, named for their frequency response. Many deltasigma devices use other filters with sinc filters for twostage decimation. Lowspeed industrial deltasigma ADCs usually use only a sinc filter.
In the frequency domain, you can see that this digital/decimator filter simply applies a lowpass filter to the signal (Figure 1b). In so doing, the digital/decimator filter has attenuated the higher frequencymodulator quantization noise. With the reduced quantization noise, the signal reemerges in the time domain.
References 

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