jj,
.) you don't understand the relation between an F.F.T. and a D.F.T.;
Yes, we all know that you claim that. What you don't recognize is the inductive definition inherent in DIT and DIF FFT algorithms. Please acquaint yourself with this basic detail.
.) you don't understand that an F.F.T. is not defined by being F.F.T. -like a blond is not defined by being blond- since that is not a explanatory definition;
Thank you for explaining that you don't understand inductive proof.
Thank you for also demonstrating that you apparently do not understand that an FFT exactly impliments the processing necessary to provide the values of the DFT of the same size.
Obviously, since the FFT DOES do so, wherever you put a DFT, assuming it's got a small prime factorized length, (i.e. the length is not a large prime), it's more efficient than the DFT and provides the same process. Ergo, the two can be equated. As one of the most famous formulations is exactly a recursive form of FFT, your claim is shown false by a very famous (but not maximally efficient) algorithm published in nearly every text I've seen. It is your inability, time and again, to make these kinds of obvious connections that seems to cause you difficulties, like those you have in "unstable digital FIR filters" and the like.
Finally, again your claim shows that woo-woo classic of "everyone but me is wrong".
No, Ion, Cooley and Tukey, Rabiner, Gold, Proakis, Crochiere, Schaefer, Smith, Akansu, etc, aren't all wrong, and they all have the actual output to demonstrate it. (I could mention some others who did things like your DTMF algorithm their first two months at Bell Labs,but I won't, I'm really NOT trying to tear you down here, rather I'd prefer that you realize you're a very junior person, with some promise, who has an enormously bad attitude and who should have been told not to make serious professional allegations against the leaders in his field by those famous French professors he had.)
Your inability to learn because of your political aggression and anti-American bigotry is, however, apalling.
.) you don't understand that U.S. imports for gainful employment immigrants with specialized skills that locals like you don't have.
You claim that the USA "imported" you to do DSP work. Please tell us who, when, and where. Provide names, places, dates. Verifiable and falsifiable, remember?
But you sure bathe in idiocy.
Let me guess:
you must be a stupid American.