4 analog signal at a rate of 2us
2us? On four channels? With calculations?
Let's do some math...
1/2e-6 = 500,000 samples per second per channel
500,000 * 4 = 2,000,000 samples per second
frequencies, energy, stability
Let's assume that each of these requires just a single floating-point math operation; a ridiculously low assumption...
3 * 2,000,000 = 6,000,000 FLOPS
I don't think even an ATmega2560 / 20 MHz is going to be able to handle that workload. You're in the wrong place.