Can i connect the tdm output with tdm input directly on Teensy 4.1?

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On the same TMD port, yes.

Normally you can only connect TDM master mode (transmitting the clock signals, as Teensy does) to TDM ports in slave mode (receiving the clocks, as most TDM ADC & DAC chips do).

But connecting the data output to the data input on the same TDM port running in master mode works, because it uses the same clocks (which it is transmitting on BCLK, FS/LRCLK, MCLK) for both data input and output. The TDM port can't know the difference between loopback of the data signal versus a real DAC and ADC which by incredible coincidence happens to measure exactly the same signal as the output to the DAC.

Connecting data signal between the 2 different TDM ports on Teensy 4.1 may or may not actually work. It probably will not be reliable, even if it does occasionally work. Even when they use same clock speed, the BCLK signals are not necessarily generated in phase sync with each other. Data loopback can only reliably work on the same TDM port.

Whatever "inspection purposes" you intend, please keep in mind data loopback uses the clock signals internally inside the chip. It can't test whether the 3 clock signal really are correct at the actual pins.
 
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