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A bit of filter theory

Discussion in 'd.i.y.' started by philiphifi, Sep 12, 2019.

  1. Jim Audiomisc

    Jim Audiomisc pfm Member

    FWIW For using digital 'upsampling' to filter, I provided a couple of demo programs and a short explanation a few years ago. The relevant page is here if anyone is interested.

    http://www.audiomisc.co.uk/software/ARMiniX/Upsampling.html

    However the snag for most people is that the software provided as examples/illusrations are for RISC OS computers. But the source code and some explanations are included. The filter 'lengths' are quite short, but illustrate the approach.
     
    Julf likes this.
  2. John Phillips

    John Phillips pfm Member

    Thanks - that's a good-looking avenue to explore. I will do so.
     
  3. John Phillips

    John Phillips pfm Member

    After a bit of thought It looks like that will provide a path connecting FIR reconstruction filter imperfections in a real context (pass-band amplitude/phase irregularities and stop-band leakage) with both filter length and filter coefficient quantization. Many thanks for the idea.

    In effect the real-world filter is decomposed into two parallel paths - a perfect sinc filter and an "error filter" which add to give the real-world result.

    The Fourier Transform is linear so I am assuming that the Fourier Transform of the error filter's coefficients will show real-world amplitude and phase errors in the pass-band and the stop-band compared to the perfect filter. I think I will dig up my GNU Octave sinc test file and modify it to see what happens.

    I'm not yet convined of that (sorry, no slight intended - it may be right but I will think on that and see what the simulation says).

    And I am not yet convinced of the central pivot point in the article I mentioned earlier, connecting FIR filter coefficient quantization with signal quantization. I still think the claim I have had quoted to me about "the only 16-bit accurate filter" is more about marketing than technology. It's no big deal but I'm just interested in understanding whether or not (and if so how) these are connected.
     
  4. Jim Audiomisc

    Jim Audiomisc pfm Member

    The effect of coeficient and calculation truncation is complicated. But by default it makes sense to be generous with the depth of the available registers/values *and* ensure you dither and noise shape the computations. The result then tends to be additional 'noise' rather than distortion.
     

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