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30th June 2012, 02:15 PM  #301  
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This way a one million taps FIR could execute in one microsecond, fast enough for six 96 kHz audio channels. Currently we have no idea how to do it because we don't know how the brain operates, how the brain stores data, and how the brain processes data. On March 15th 2012, French scientist JeanMarie Souriau died. From 1960 he kept suggesting that we are not in the reality. He kept suggesting that we were equipped with hardwarecabled "group engines" from a mathemetical conception, acting as perception devices. He kept suggesting that mechanical engineering is a mathematical group (groupe de Galilée), that relativity is another group (groupe de Poincaré), and generalized relativity is another group. He kept suggesting that we, as living organisms, we are trapped into particular, complicated sections of "hidden groups". The whole geometry discipline, is now considered as a mathematical group, indeed. According to JeanMarie Souriau, from a geometrical and mathematical perspective, time and energy can be manipulated, annihilated, using particular group sections to be seen as geometric sections. In an interview dated December 27th 2010, he said that monkeys have abilities that the human don't have, because they have a better "Euclidian group" cabled in their brains. In the same interview JeanMarie Souriau said that some day, mathematics, geometry and physics will meet in the neuroscience playground and generate huge progresses, but it won't happen rapidly because those sciences are usually kept apart. A very optimistic theory  nothing to do with JeanMarie Souriau words here  would be that once you manage to operate the correct geometric transformation, you end up like "virtually" connected to the "reality", hence able to manipulate time, space and energy at will. There are peoole saying that the human can be persuaded doing this, by accident (near death experiments), by drugs (DMT), and possibly later on, by science. You'll find always people ready to say that a copper wire has an infinite digital processing power because it permanently executes a 1million sample FFT then inverse FFT on the signal he is conveying, taking the required energy from nowhere, and exactly compensating the inherent delay by executing in the future. Or in the past? This is only about a copper wire. Imagine what they would say about a whole brain. Gosh, I'm completely lost! Last edited by steph_tsf; 30th June 2012 at 02:25 PM. 

30th June 2012, 02:24 PM  #302  
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For you Abralixito: a FIR is a convolution denoted y[n] = x[n]*h[n] y is the output, x the input and h is your filter. n is the time index, and * is the convolution operator. In order to make it in the frequency domain, you compute first the Fourier transform of x and h: X = F(x) and H = F(h) The convolution in timedomain translates into a simple multiply in the Frequency domain: Y = X . H where Y is the Fourier transform of your output and '.' is the multiply operator. All you need to do now is to compute the inverse Fourier transform of Y in order to recover the timedomain samples. So the global operation is: y[n] = invF(F(x[n]).F(h[n])) Now what's the fuss? Well, direct form of convolution is power hungry, and required resources grow with *square* of the length of the filter. The domainfrequency convolution, despite of looking complicated, is much less power hungry if you compute the Fourier transform and it's reverse using a FFT. Hope it makes sense! 

30th June 2012, 02:30 PM  #303 
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30th June 2012, 02:30 PM  #304  
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30th June 2012, 02:44 PM  #305  
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Most of the time, there will be a Bode plot (gain and phase) associated to a given speaker driver exhibiting a 2nd order highpass at something like 100 Hz (Q maybe 1.0), a few semirandom inband irregularities in a 6 dB corridor from 100 Hz to 5 kHz, possibly a +10 dB resonance at 5 kHz, then a quite irregular lowpass above 5 kHz, possibly 3rdorder, with a few high frequency resonances corresponding to the cone breaking up. Most of the time, the designer ambition is to reshape the Bode plot, for attaining a desired Bode plot like a nice 4thorder double Butterworth highpass at 300 Hz and a 4thorder double Butterworth lowpass at 3 kHz, with the phase exactly matching a minimum phase behaviour. The direct FIR method is very simple : you graph the actual driver impulse response, you graph the idealized driver impulse response, and by comparing them, you know the FIR coefficients that you need. You apply a windowing function, and you are done. Basing on this, how would you calculate the FFT coefficients (real and imaginary) for generating the exact same filtering function, both in magnitude and in phase? Say we apply a 1024 point FFT at 48 kHz, leading to a frequency resolution of 47 Hz. Is the FFT + FFT1 feasible, realtime, on a CortexM4 clocked at 72 MHz? Last edited by steph_tsf; 30th June 2012 at 02:54 PM. 

30th June 2012, 02:51 PM  #306  
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It's not my purpose to show anything  I just reacted when CuTop was accused of trolling, which he wasn't. Sorry if I let you think I was trying to demonstrate something. Now re. the FFT on the ARM, I know there's a DSP library from ARM themselves. There should be a FFT in it, and if it's the case you even won't have to implement it 

30th June 2012, 03:04 PM  #307  
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h[n] = h[0], h[1], ..., h[M] where M+1 is the length of your filter Your coefficients are simply the Fourier transform of the sequence h: H(k) = F(h[n]) Quote:
Now why do you want a 1024point FFT? Let's say your original filter is a 1024point sequence. You can always split it into 8 successive 128point sequences and thus use a 128point FFT... 

30th June 2012, 03:08 PM  #308  
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Since you clearly know a fair amount about DSP, do you have any answer to my earlier posed question about roundoff errors in FFT convolution when using fixed point and how those compare with FIR convolution? I'm curious to know whether Dr Smith's arguments hold up for fixed point.
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30th June 2012, 03:13 PM  #309  
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I have the impression that your assertions are correct on a mathematical point of view, but completely discoupled, and potentially wrong, when it comes to the physical application. 

30th June 2012, 04:16 PM  #310  
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It's a real dilemma in these forums. There's an interesting sounding thread about DSP and active crossovers called "Open Source DSP XOs". It doesn't mention "No PC allowed". It doesn't mention "No FFTs allowed". There's 29 pages of stuff about specific hardware, and the difficulty of implementing a simple crossover with any number of esoteric processors. Whereas I've got a system running on a PC using my own software which can implement millions of FIR taps. Personally, I'm using 65536 taps for each of my six channels and the PC isn't even breaking into a sweat. Why shouldn't I ask why people aren't doing the same thing? Mine is an "Open source DSP XO" (anyone is welcome to my code if they ask nicely) so I'm not even off topic. Ah, but didn't I know? No FFTs and PCs are allowed in this thread because everyone here knows there's something mysteriously wrong with that approach. Eject the outcomer as a troll! But then it turns out that some people here, at least, don't know about FFTs and how they can bestow upon you virtually unlimited FIR processing power. Maybe there is some theory about 32 bit floats not providing enough precision, but why not use 64 bits instead? Your PC can do it! But anyway, I'll leave you to it. Good luck! 

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