Is it possible to select the polarity of the 9361's ADCs? As in, select whether data captures on either the rising or falling clock edge for a given channel.
What you mean by polarity of ADC?
AD9361 is a transceiver chip and data from both channels is multiplexed and sent on port depending on configuration.
Various configurations are supported by AD9361 for more details refer UG-570 digital interface specification.
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