Twenty years ago, I programmed am SBC to do FFTs, in assembler and FORTH. Of course, on a 2MHz 8080, each calculation took a couple of seconds, so it was nowhere near real-time. My point is that the algorithms are out there.
But doing an FFT (and then a window discriminator) seems like a lot of work to make a frequency- sensitive strobe trigger to process what I'm assuming is an audio input. People have been making strobe boxes for decades, and I guarantee they weren't using FFTs explicitly. Search on frequency sensitive audio circuits, which are more commonly called filters. E.g., you would feed the same signal in parallel to multiple bandpass filters having different center frequencies, with the output of each filter set up to trigger a strobe when substantial energy appeared at that filter's center frequency.
You can learn a lot doing the job with analog components.
You can also probably find a single chip that will do most of the work, but you'll learn less from the experience of plugging it in.
I'm pretty sure you can also do this stuff with DSP chips. I have a sample board here somewhere; I should mess with it before it dies of old age, or I do.
Mike Halloran
Pembroke Pines, FL, USA