jj@alice.UUCP (05/30/86)
> From ...!nbires!nbisos!todd Wed Dec 31 19:00:00 1969 > > > In respose to jj@alice.UUCP: > > I thought it was in the neigborhood of 96 samples in the filter at > a given time, with 24 of the original samples (samples from 44.1 K > stream) used. There are typically 96 taps and 96 constants used as > multiplication coefficients in a 4 X oversampling digital filter, > not 384 (96*4). You are in fact correct. You have also reminded me that the original Phillips technique isn't quite as good a filter as should be used. I did a Remez exchange filter generation of a 96 tap filter, and got about 50dB rejection, so since I recalled the 96 tap number, I figured that it was the multiply-add count, not the filter length. Oh well. Next time, Phillips, make the filter a bit better (It really may not matter very much at all to the ear, though, since all the error is at above 22kHz, and is quite far down.) > ...<strange interpolation method deleted> > > I think that the results here would give a lower average difference > in transitions between each of the filter's outputted samples. It > ... > the multiplications to the sums of 2 samples. This requires use > of only 48 multiplies for a given final output, compared to 96.> > > It appears to me, that when using 24 samples, each inputted once > to a 96 tap filter, four different impulse resposes will be present > for four sets of 4:1 interlaced data streams. If every fourth Um, no, you have ONE output data stream. If you look at the ONE data stream, in order, you find that you get exactly the impulse response of the filter, representing a band-limited (to 20kHz) pulse, which is what you SHOULD get. It's also linear phase, since the filter is symmetric. > sample of the 176.4K stream was demultiplexed out of the stream, > that new stream would have a unique filter characteristic (defined > ... > outputted samples might become large in magnitude. Does Phillips > "noise shaping" following their digital filtration help this situa- > tion (if this case really exists)? Or, is it left to the analog low > pass filters following D/A conversion to filter out what may be high > energy ultra-sonic frequencies resultant of these differences > between outputted samples. You're wrong. I don't know where you err in your thinking, but you are in fact wrong. There's nothing either cheating or magical about the many multiplies by zero. It's a simple filter. Nothing more. The filter happens to remove anything that is above 20kHz, and that's it. If there is, as you put it, a "difference that is large in magnitude", that difference represents, by simple principles of DSP, something that has no energy to speak of above 20kHz, and also something that is in the original signal. DAC's, by defination, don't filter. <Unless they aren't working right!> > ... > (so all four might be considered the same impulse response sampled > in slightly different time frames), but they each still differ. But why look at them separately? There's no reason to do so, since the relevant information is the ENTIRE data stream! > ... > 96 tap filter (performs all 96 multiplies by all inputted data) > would produce given the same narrow pulse as an input. Would this > hold true in other cases (with complex waveforms) as well? No. You talk about "true" interpolation, etc, but you're simply making,from my viewpoint, a time-varying filter that's NOT easily represented mathmatically, and that's not going to do the necessary anti-imaging (alaising) filtering, unless you just happen to choose 96*4 coefficients for it that make it a 96*4 tap filter with 3/4 zeros in it! <Something familiar here, eh?> Of course, you'd have to hold on to 96 samples, NOT 24! > ...<much confused illustration removed> > > will take in a 176.4K sample width impulse instead of the original > 44.1K sample width impulse? (CD test disks are available with such > impulses digitally encoded on them.) The question is confused. Yes, it's entirely proper to have a single impulse at the 176.4kHz rate, and it seems obvious enough to me that I can't guess where you go wrong. > > .......................... and zeros are put between the known samples > > for several other reasons as well... > > One of these reasons is cost reduction and simplification of digital > filter design (only ~24 samples need be processed at a time). I Horsepuckey. There's nothing a bit cheating about putting in the zeros. The technique of interpolation often results in such economies, but there's no cheating or loss of information to it, as you seem, to think! In fact, adding the zeros has a very nice, tractible, and demonstrably effective result. > would love to know what the other reasons for inserting zeros between > samples are. (So anxiuos to know that it excedes my ability in finding > time soon to research texts at the library. :-)) Well, mostly, it raises the samplng rate, and creates the images of the signal centered around multiples of the old sampling rate. The filter (interpolator) removes the images. Simple. That's all. No magic. No cheating. > > ............. Rabiner and Shaffer, or Rabiner and Gold, or > > Oppenheim and Shaffer, have all written good texts that will explain > > this to you. Please go to the library and read one of them. > > Thanks for your response, jj. I appreciate the references to these > texts. Although it will be a while before time permits finding them, > I surely will research them when I can. Please do. I think that we shouldn't discuss this more on the net. The article sizes are very large, and I suspect most people don't care. Mail me directly. Do bear in mind that I also have work to do, and others have written texts, so I don't want to write one here. -- TEDDY BEARS UNITE! SAVE YOUR FUR TODAY! "Gravity causes the stars to shine, tropisms make the ..." (ihnp4;allegra;research)!alice!jj