Plotting FFT on arduino

Currently, for generating FFT using ACS712 current sensor, i use the following method: the data from the sensor is sent to processing IDE via arduino. the processing generates text file which is then loaded into Matlab for generating FFT. Is there a way for generating and plotting FFT on arduino itself?

Sure, have you got a screen for the Arduino?

It may be worth having a Mega as the extra RAM is valuable for a project like this (better FFT resolution with more bins). Of course its not the simplest project, you might have to do a few simple practice projects using a screen first.

A long time ago I did something similar on a 3.2" TFT: