I think that you have to eat your politically correct words of "...bigot...", "...misleading...", "...oozes...", don't play being an authority and learn Goertzel, jj.
Excuse me, are you accusing me of faking being an authority here?
You have already been shown a liar when you claimed that you could not establish my credentials. It's been available to you from the start, and you appear to have failed, even now, to check what's trivially available to you.
Now, you attempt to futher your anti-american bigotry by smearing me, rather than admitting that this american from a second-class background, the FAT american from a second-class, appalachan background, is entirely superior to you both in terms of the history in this context and of fairness in presenting that history.
Until you admit that, I will make sure that everyone here realizes the utterly bigoted, lying nature of your ignorant, provincial attitude.
That algorithm that I submitted is the Goertzel in D.T.M.F. Detection.
No duh, and that's all it is. You implied in your attempt to sieze credit from Cooley and Tukey (and some others) that it was a full FFT and we both (and so do some others here) know that's just not the case. (NB,I knew that at the beginning, but I was curious to see if Mr. Ion here would admit to his deception. It appears that he's still trying to cover it up instead.)
You were grilled about this. You didn't, haven't and STILL won't admit your original statement was biased beyond reason and constituted a theft of academic credit.
DTMF detection, as we both know, is a widdle teeny tiny part of the art and practice of signal processing. Yeah, it's useful, but the fact that Goertzal is useful there is just that, no more and no less. It does not and can not make Goertzel a full, efficient FFT.
For an N-point D.F.T., N*N complex coefficients are needed.
Stop obfuscating. We're talking about an FFT, not a DFT. We're not talking about a full convolution, NOBODY does that, we're talking about an FFT.
How many coefficients does an FFT require. Fess up, child, fess up.
They appear in my opening post as how they come from a D.F.T..
DOH. You keep repeating this meaningless fact as though it has some relevance on the issue. There are about as many ways to implement ONE LINE Of an a FFT as there are people doing it. On the other hand, Goertzel is quite the good way to do ONE LINE FROM AN FFT. Nobody is arguing that irrelevant, simple fact.
I'm surprised you haven't brought up the 2D retrace method, too. Oh well, I won't do your homework for you.
What I am pointing out is that your claim that it was faster than an FFT, in an unqualified statement, was simply wrong. It was wrong, it is wrong, and it will continue to be wrong.
Now that you've noticed that an FFT for an entire transform is a whole lot simpler, you are trying to slip by a DFT instead of an FFT. Your weaving, wobbling, and evasions are just pathetically obvious, and your malicious intent in not capitulating entirely to my entirely correct and incotrovertable analysis of your nonsensical claims is looking to be willful.
The Goertzel algorithm can be taught as a second-order I.I.R. filter, except that one output result is generated after N input samples.
Irrelevant. One output, many outputs, etc, it's an IIR implimentation, with all of the headaches, problems, and advantages thereof. The fact you sample it once evern 'N' samples doesn't matter, you have to RUN the whole thing, not just one sample, in order to GET that last sample. Such are IIR's.
That's why FIR's are so much more useful for SOME applications, like for instance decimation/interpolation (but not in all circumstances, of course).
F.F.T.s being based on decomposing D.F.T.s of a sequence of length N into smaller successive D.F.T.s,
No, that's FFT's not DFT's. Even a second's reflection would show that. There is even a recursive method that makes that stunningly clear, although its not the fastest or cleanest method.
it is true that Goertzel in 1958 got a computation of 2*(N+2) real multiplications and 4*(N+1) real addition, before and faster than Cooley and Tukey in 1965 with F.F.T.s computations of N log N computing all the values of the D.F.T..
IT IS FASTER FOR ONE LINE.
Now you shall capitulate fully, and agree that the FACT is that Goertzel is less efficient when you need the whole transform. That's how it is, was, and will be. Goertzel runs as proportional to N*M where N is the number of samples, and M the number of lines.
For the reader, here is a good web reference, showing in nice, simple print the outright lies that Ion is trying to pass off here.
http://ptolemy.eecs.berkeley.edu/papers/96/dtmf_ict/www/node3.html
Now learn Goertzel (Germany), standard of the D.T.M.F. Detection in U.S.:
We've agreed that it is reasonable to use for DTMF. What's your problem. Your telling ME to learn an IIR filter is chutzpah of the highest order, as well as implicit libel, sir.
there is no more excuse to be illiterate after I showed you the way, in spite of your claim to be a U.S. specialist of F.F.T.s.
I advise you to retract that.
Goertzal like you write doesn't exist, so I repeat for your very slow learning that it is Goertzel.
.exp(-j.k.pi/N)
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