Regarding:
I advise you jj to go back to school -preferably in Europe- and learn it.
I require your admission that I haven't said anything incorrect, and that you stalled, stalled, and stalled some more, and have yet to fail to admit that Goertzel is not an FFT.
You have repeatedly misstated what the Goertzel algorithm does. I have cited a helpful document to you, but you have yet to acknowledge your utterly wrong positions.. As you continue to repeat them, they become deceptions merely because you have failed to do due dilligence, if nothing else.
Including the fact that an algorithm for computing D.F.T. is Goertzel.
One instance of Goertzel calculates one line of a DFT or FFT. We agree on that. One instance of a Goertzel algorithm does no more or less than that.
Unless we use it as an N^2 algorithm it will not calculate a whole DFT or FFT.
in
http://www.ece.utexas.edu/~mason/codesign/pass/embedded.html
it says very clearly "Goertzel is not considered a Fast Fourier Transform (FFT) because it is order n2, not order nlog2

. "
With less than N log N.
Your statement is false. The quote above clearly shows that. Goertzel is, as the web reference, or basic understanding shows so clearly, less efficient unless you only want a FEW output lines.
You have admitted this, yet you continue to deceive and say "less than N log N". You know, I know, we all know that it can't do anything close to N log N for anything more than a few lines, let alone an actual transform.
Why do you continue to make this lie, sir? You are fully found wanting by every reference available.
No matter your ignorant semantics of "...partial...:, etc.
Blah, blah, blah.
You have repeatedly attempted to pass off an algorithm that calculates one line of a transform as the whole transform.
You are going to have a whole lot of trouble figuring out a spectrum from one line, you know. Need we go into Parsival's Theorem, etc, to point out the misuse you are making of the word "transform"? Please explain to me how your 8 lines are 1:1 and onto. Oops, they aren't. Ergo, they aren't a transform. You knew that all the way from the beginning, too.
You know your statement is a lie, sir, and yet you continue. Again, let us cite a handy internet reference:
http://www.cambr.uidaho.edu/papers/fft_on_rdpp_slides.pdf
Where, in the process of explaining a case where Goertzel is USEFUL, clearly states that Goertzel is O (n^2) and the FFT is O(n long n). Goertzel, while it has its applications, is, as this and every other reference we've cited at you shows, is O(n^2) for an actual transform. This paper is even, due to a particular processor design, espousing the use of Goertzel, and it says clearly that it is inefficient in terms of calculation.
You use it in DTMF as a set of filters in a filterbank. Fine, but don't claim it's any kind of DFT, you've just taken some DFT basis vectors and used them as a matched filter. You aren't even doing a transform, just running a filter bank. It's a good filter bank, but that's all it is.
As it clearly points out in
http://www.mathworks.com/access/helpdesk/help/toolbox/signal/goertzel.shtml again you are wrong in asserting that it's faster for an actual transform. Quoting:
---
Note fft computes all DFT values at all indices, while goertzel computes DFT values at a specified subset of indices (i.e., a portion of the signal's frequency range). If less than log2(N) points are required, goertzel is more efficient than the Fast Fourier Transform (fft).
----
Once again, it states clear that if you need a transform, not just some bits and pieces (useful though they may be), Goertzel is not faster for any realistic size of transform. It may be useful on a painfully specialized processor, but again that's not the claim you just made, you just again fallaciously said
With less than N log N.
Which can be seen to be wrong by inspection.
It can be seen wrong via any of a plethora of net references, or references in books, papers, etc.
You are, once again, shown to be completely wrong. Your claim is false.
You are attempting to cover your theft of academic credit from Cooley and Tukey with this absurd smokescreen.
Mind you, considering BTox and WildCat, you show promise.
But not good enough...