Protective relay with Raspberry PI (doubts)
I wouldn't use Rasbperry Pi for your project. I would probably only use an arduino for both ADC input and digital output.(I'm not an expert of dft calculations so I assume that speeds of arduino boards would be enough for it.)  

Arduino's(Uno/Nano) ADC speed is about 10 kHz according to official reference website: https://www.arduino.cc/en/Reference/AnalogRead , so it could be sufficient for your your situation (960*6= 5760 reads per second) if other operations won't delay the program too much.

About the output response; you can use timer interrupt for a constant 240 sample per second. Here is a tutorial example of arduino timer interrupts: http://www.instructables.com/id/Arduino-Timer-Interrupts/?ALLSTEPS

As I mentioned before, I don't have much knowledge about your suboperations(dft etc.). So if you need more operation speed, you can always look for improved boards like Arduino Due or Zero instead of Uno/Nano.

Here are some information to improve ADC speed for both Due and Uno/Nano:
http://www.microsmart.co.za/technical/2014/03/01/advanced-arduino-adc/
http://www.djerickson.com/arduino/