If you get the data via UART, then the dump from the terminal program could be used after some "conditioning", like number formatting. I'd assume that the ADC is connected to "something" you can use to record the waveform, even an oscilloscope could help if it has something like a USB port and enough sample memory. Here you may have to elaborate a bit how you generate the signal and how you capture it. For test purposes, you can just generate the waveform in the pc with a program/script. Once the algorithms work, you can switch to work on the real signal.