you may be able to process audio using a Teesey, ESP-32 or a Due
https://www.pjrc.com/store/teensy32.html
or a Raspberry PI?
to sample 10KHz you would have to acquire minimum 20000 samples/second
how many ADC bits are you planning to convert?
how are you transmitting the data to the PC?
you could sample the audio on the PC and transmit the results to the arduino for display?