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18th July 2012, 10:48 PM  #101 
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Join Date: Feb 2008

Ah, thanks. I keep getting thrown by the reference to "standard". What you have there appears to be an approximation of the magnitude response of lowQ analog filters, such as Bessel or Butterworth. While those filters are standard, that approximation is not one that I have seen in common use, at least not for higherorder filters.

18th July 2012, 11:13 PM  #102  
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18th July 2012, 11:39 PM  #103  
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Edit: maybe what I've just said means no sense at all in dBs and log frequency scales, but it looks quite clear to me on the linear/linear scale. Last edited by CopperTop; 18th July 2012 at 11:45 PM. 

18th July 2012, 11:52 PM  #104  
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19th July 2012, 12:13 AM  #105  
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My procedure is to calculate (or draw, or whatever) the desired frequency response and load up the FFT with it (real only, imaginary set to zero for a linear phase filter, symmetrical about the Nyquist point, DC and Nyquist elements set to zero), then I calculate the inverse FFT to get the impulse response. I window that with a raised cosine whose width is proportional to the FFT size. Then I calculate the forward FFT again and use the result as my filter in the real time crossover program (which is implemented using overlapadd, incidentally). I also plot the frequency response only after the windowing which, for a large FFT is usually pretty much identical to the input  when viewed on a linear scale at least. Until now, I've been using the window purely to allow me to specify any frequency response I like without worrying about discontinuities at the edges, rather than attempting to use it the other way round i.e. to influence the frequency response. Steph also mentioned the idea of using the window as the tool for reducing ringing and overshoot some time ago. Thanks, I will look into it. 

19th July 2012, 12:26 AM  #106  
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Ultimately you will find yourself trying to find a compromise between rounded corners, steep transition band, and attenuation above 4 kHz. (Again I suggest that you also examine your frequency responses on a dB scale.) Quote:


19th July 2012, 12:52 AM  #107  
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20th July 2012, 09:39 AM  #108 
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@gberchin
I haven't got round to anything more advanced yet, but I did try simply reducing the width of the raised cosine window that I multiply the impulse response with. This does, in fact, result in the rounding off of the corners of the linear crossover. Presumably, the ultrasharpness of the corners was possible because of the low amplitude, but extended, ringing on either side of the central impulse which is now gone. I enclose a screenshot of the new rounded linear crossover, plus a 'standard' filter with a similar level of suppression of the frequencies at the edge of the crossover region. I'm thinking that the rounded linear crossover is a pretty good compromise. A bit light on details, I know, but I'll endeavour to pull it all together with better onscreen stats and those log scales! 
24th July 2012, 11:49 PM  #109 
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@gberchin
Finally some plots with log/log scales. (More prettifying to do yet, though) The 'standard' crossovers are as the formula mentioned previously (Q = 0.5). The Gaussian is as per the formula you supplied a few pages ago. The experimental linear crossover is shown with a wide window i.e. sharp corners on the lin/lin plot. I can switch/sweep between shapes, cutoff frequency, order and window width in real time while listening to the result. 
25th July 2012, 02:45 AM  #110 
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compare with iDFT_Lab
see attached .jpg and .zip 
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