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25th July 2012, 08:46 PM  #111 
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I think we're on the same wavelength, so to speak. I enclose a screenshot of another filter type I've included: the Chebyshev* (but it's not obvious I've gained much by it, in terms of selectivity vs. ripple and overshoot).
Chebyshev filter  Wikipedia, the free encyclopedia Steph, a while ago you were talking about numerical methods for optimising the filter. Could you just go over how you envisage that working? I think you were talking about starting with a basic prototype impulse response, and adjusting a window to influence its ripple and the resulting frequency response for optimum measurements. *Ripple factor in this case 0.01 cutoff frequency is not the usual definition, which complicates things a bit 
26th July 2012, 01:32 AM  #112  
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Afterwards I did iDFT_Lab. Using iDFT_Lab I realized there are many degrees of freedom, especially when you can arbitrary define the lowpass sharpness (Brickwall  Asymptot  Butterworth  Bessel) and lowpass slope (equivalent from 1st order to 6th order). You can consider "my" Asymptot as "your" Cheybychev. This is the advantage of the iDFT approach, cleaner than Cheybychev. A nice generalization would be to define a "sharpness" parameter that's continuously variable, allowing to go from Asymptot (max. sharpness) to Bessel (min. sharpness), as target lowpass. Then introduce the "equivalent order" for defining the slope. Any idea welcome. As usual there is no free lunch. The sharper the transition band, the longer and more intense preshoot and ringing. I have included the "double" option for emulating all LinkwitzRiley amplitude behaviors, when selecting the Butterworth sharpness. Very important is to keep an eye on the complementary highpass slope. Due to the fact that a Bessel lowpass is close to Gaussian (especially high order Bessel), we see that all complementary highpass built from a Bessel lowpass are only 2nd order. Which is insufficient in most practical cases. I tried refining iDFTLab, adding an auxiliary highpass on the higpass (needed when the highpass slope is only 2ndorder), but that's far from easy when asking for a pure LPF + HPF reconstruction. What you take out from the highpass, you need to give it back through the lowpass. This implies a second DFT + iDFT stage. Such feature is not yet enabled in iDFT_Lab. The FIR length can be quite short when operating at 4 kHz or so. For a 4 kHz crossover operating at 48 kHz, I would never exceed 101 taps, and just like Philips did with their DSS930 back in 1993, a 31tap FIR seems to work pretty well. One could take twice this length as basic quality improvement (20 years now from Philips DSS930), and again twice the lenght for accomodating a 2 kHz crossover frequency instead of a 4 kHz crossover frequency. A 121tap FIR seems thus adequate, in 2012, for a highly flexible FIRbased crossover operating at 48 kHz. Now if the system is running at 96 kHz, we'll need a 301tap FIR. Operating at 96 kHz, if wanting to apply a high resolution amplitude + phase linearization, individually applied to all speaker drivers along with the crossover function, the FIR needs to be much longer, something like a 601tap FIR. Now it's time to design an allin one system, WinXPbased, doing the high resolution amplitude + phase linearization along with the crossover function. Also enabling a few IIRs, assisting the linearization FIR. I'm attaching as .zip the various tools I have developed. They are quite handy, enabling to taste the digital reality, intuitively. 

26th July 2012, 09:25 AM  #113  
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26th July 2012, 10:21 AM  #114  
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FIR_Lab indicates that your "high order Gauss" may be a 61tap FIR Sinus cardinal (having a certain natural frequency) windowed by BlackmanHarris. As soon as you introduce Gauss as supplementary window (try FIR2 on FIR_Lab and play with the Gauss width), your highpass slope decreases. FIR_Lab enables to replace any FIR by a rectangle window. This way you can determine who (FIR1, FIR2 or FIR3) is actually governing the FIR spectral behavior. See the attached files. 

26th July 2012, 10:44 AM  #115 
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In iDFT_Lab, use Asymptot with Blackman windowing for emulating Chebyshev. As you can see, a 81tap FIR is adequate. See attached .jpg.
Last edited by steph_tsf; 26th July 2012 at 10:48 AM. 
26th July 2012, 11:12 AM  #116 
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Have you considered the Philips DSS930 setup dating back from 1993? See attached .jpg.

26th July 2012, 06:36 PM  #117 
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make sure you use the most recent versions of my tools, as I recently made a few cosmetic changes in the wording of some dialog boxes
see attached .zip 
27th July 2012, 12:23 AM  #118  
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I have to admit that I have yet to come to terms with the motivation behind all these filter types! For example, the Bessel which you mention appears to be notable because of its constant group delay across the pass band (thanks Wikipedia!). Presumably, though, this is not a factor in a linear phase implementation..? The maths behind Bessel polynomials and Chebyshev polynomials etc. seems to be quite mind boggling, yet the end result, in a linear phase filter form at least, is quite mundane. If we look at this Chebyshev polynomials  Wikipedia, the free encyclopedia it is clear to me that it would take the rest of my life to develop the mathematical skills to write that page. But what would be my motivation to write that page? Yes, it's the motivation behind the filter 'brands' that I'm not sure of. As far as I can tell, it is possible to 'dial in' a desired frequency response, and suckitandsee what you get in terms of the impulse response ringing. No real maths involved. If that doesn't meet your various criteria, you can then massage the frequency response iteratively until it does. And give up if it doesn't. Or, alternatively, it might make sense to tweak a window around the impulse response in order to more directly attenuate the ringing ampltude/duration. You can then see what you get in terms of frequency response. Again, no maths involved, really. Or you could convolve the frequency response with a window to smooth off the sharp edges, and see what that gives you in terms of impulse response. Maybe the maths is significant for analogue filters (who could argue with the properties of the Butterworth?), but the digital linear phase filter seems to set us free from the maths. (Happy to be corrected on this!) Point for discussion: my naive 'linear crossover' gives excellent attenuation of frequencies at the outer reaches of the crossover region, but visibly low amplitude ringing and overshoot around the central impulse. The ringing, however, extends for a long time albeit at a very low level. We could 'round off the corners' of the frequency response directly (as seen on a lin/lin scale) to reduce the duration of the ringing, or we could window the impulse response to achieve the same thing. But in short, if we're designing a digital crossover filter, why do we need the maths and the filter 'brands'? (You mention the Philips DSS930. I would be happy to try to emulate it. However, I think you said that it is '2.5' design so I would need to acquire some sacrificial 3 way speakers  not a problem, and also that some of its desirable characteristics stem from the physical response of the drivers being combined with the crossover characteristics. As I mentioned, I have my calibration microphone ready (and yes, it's built from a Panasonic WM61A capsule  I bought a few some time ago) but it will be a gradual process until I am designing the optimum speaker, I think. Do you possess some DSS930s? Do they sound as good as the theory suggests?) 

27th July 2012, 03:14 AM  #119  
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What a mess with Philips! We can do better using modern inexpensive components. For a quality d'Appolito, you need to reduce the distance between the two sound sources, hence the reason for selecting the Dynavox DY166 as bass drivers. A minimal distance between them is possible thanks to the new Datyon 16mm and 20mm mini tweeters available on eBay Germany (Dayton ND16FA6 or Dayton ND20FA6). Those mini tweeters should operate with a 3.0 kHz crossover, say the Butterworth 6thorder that we have already sketched, providing symmetric lowpass and highpass 6thorder slopes. Start using those speakers as closedbox satellites only covering 120 Hz to 20 kHz. Allocate your full attention to precisely combining the linearization function and the crossover function in each FIR. Use IIRs, assisting the FIR whenever possible. Later on, buy four more DY166 bass drivers, convert all of them them to MFB, and you'll be astonished by the results. Now you have standalone compact speakers for domestic listening levels covering 30 Hz to 17 kHz in a 2 dB corridor, producing no distorsion in the deep bass range. The only Achille's heel of such concept is the woofer directivity pattern. The DY166, at 3.0 kHz, starts beaming, while the 16mm or 20mm tweeter, is still radiating wide. This is not optimal. You may try reducing the crossover frequency, say to 1.5 kHz, chack if the tweeter doesn't some nasty overcompensation, gain and compare the subjective results. The next step is to go 3way. You will reuse the four DIY166 MFBequipped as 30 Hz to 150 Hz bass. For the medium between 150 Hz to 3.0 kHz, you need to buy four Fountek FE87 drivers on eBay Germany. Each satellite to be a d'Appolito carrying two Fountek FE87 and one Dayton minitweeters. Crossover frequency 3 kHz. At such frequency the Fountek FE87 and the Dayton minitweeter are still radiating wide. Last edited by steph_tsf; 27th July 2012 at 03:44 AM. 

28th July 2012, 03:06 AM  #120  
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