In the original FFT based project, I was very much resource constrained. I read PIC has some nice DSP features, so my original plan was to use a dsPIC.
However, sampling from Microchip took way too long, so by the time they arrived I had already started with an Atmega328. Due to the new algorithm this turned out to be okay.
I also learned later that PIC does 2 cycles per instructions, so the 40MHz is about the same as 20MHz AVR.
I transferred the breadboard circuit to stripboard, and did more testing. This seemed promising, so I proceeded with designing the PCB.