It seems to be reasonably well accepted that Sigma-Delta ADCs have much looser requirements for the anti-aliasing filter due to both the noise shaping and high modulation frequency.
However, it seems to implicitly assume that the input signal is continually sampled by the converter. Many sigma-delta ADCs such as the TI ADS1256 and Analog Devices AD7192 have an input mux.
Let's assume that four signals are connected to the mux, and each is given one quarter of the time on the actual converter.
With the mux, the signal is no longer being continually converted, but is being sampled, albeit for long periods of time. Since it is no longer being continually integrated, how does this affect the anti-aliasing requirements for the converter? Is there a reference that goes through this case in detail?