storing data from ADXL345 with high data rate on sd card and FFT


I was wondering is it possible on arduino (uno/mega) to log data from ADXL 345 with 3200hz data rate on sd card and make FFT in the same time.
I think there might be a problem with limited memory in microcontroler. Is there any way to overcome this problem ? Is it possible for other device (for example rasppery pi)?

That is too much for the normal Arduino boards.
The Arduino Due is a lot faster, but the Due still like a normal Arduino without an operating system, memory managment or file system.
The Raspberry Pi should be able to do that, or perhaps you can connect the sensor to a computer with some kind of interface.