STM32 controlled PI detector

[cristiano.sar]

I'm trying to build a Stm32 controlled Pi detector. Until now, I have made the TX part and I'm now in the step of reading the ADC data to detect metal and ignore the unwanted signals (EFE, GB, etc).
The MCU I'm using is stm32f407xx and I'm using one of its internal ADCs (ADC1) with DMA transfer.
My doubt is if I should make ADC readings at specific time windows (for example, 10us after TX pulse ends like in regular Analog detectors (sample delay)) or if I should use the DMA in circular mode and make some kind of calculations to check at what moments look for the relevant signals.

Below is a capture of 64 samples of my ADC with DMA in circular mode:

Below is a capture of 64 samples of the ADC in normal mode, captured after a delay of TX pulse end (seems a little strange to me):

I have experience with programming with high level languages but not with low level (in embedded systems) but I'm learning and also getting some help from AIs.
Thanks.

[moodz]

I would rrecommend to sample synchronously.
... all ADCs basically have a modulator at their input so if you sample asynchronously you are looking at the product of Fo and So where Fo is your signal fundamental Tx Frequency and So is your sampling frequency.
If this product falls within your target passband then you will get uwanted side effects in the data.
Oversample and integrate for best results.