Yes. Some slight lacks of precision, but very clear and well written. His naive filter sucks, though :-).
BTW, the Cooley-Tukey algorithm only bears this name due to one of those small decisions that sometimes change the course of history. The episode involves another great man, and a good friend of John Tukey: Richard Hamming. I'm not telling the story here (no time and no beer), but if suffices to say that the algorithm would have been named Hamming-Tukey, had not Hamming done what he often referred to as his biggest act of technical misjudgment. I only met Hamming some 20 years after the episode, and Hamming was still brooding and mourning over it (but in a happy, laughable way).
And it was for the best. Cooley got his place in the history of science, with what has often been considered one of the ten most influential numerical algorithms of the century, and Hamming still maintained his own place(s), with the Hamming window, Hamming codes, Hamming distance, and some other relevant results in numerical analysis. He also secured a place in my memory, for what it's worth.
Best
Paulo
