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Length of FIR filters

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  • Uli Brueggemann
    There is no lunch for free. IIR filters require much less parameters in general. They are good for minimumphase correction (correction of amplitude response)
    Message 1 of 1 , Jun 1, 2012
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      There is no lunch for free.

      IIR filters require much less parameters in general. They are good for minimumphase correction (correction of amplitude response) but NOT for excessphase correction. To get stable results in manyt cases IIR filters are cascaded biquad filters. This may introduce noise in case of a low precision of number format.

      The frequency resolution of a FIR filter is given by the ration samplerate/filterlength. Indeed is is not mandatory to have a finest resolution in the higher frequency range. But it is a big difference to have e.g. 1 Hz resolution in the frequency range below 100 Hz or to have just 20 Hz resolution !

      There are two possibilities to get the fine resolution in the lower frequency range:
      1. split the frequency range in several areas and use a different samplerate in each area. It is common to use 96 kHz and then to downsample by power of 2. So you will get 48 kHz, 24 kHz, 12 kHz, 6 kHz, 3 kHz, 1.5 kHz Hz. The last example allows frequencies up to 750 Hz but under practical aspects you may use frequencies up to 300 Hz. With a filter length of 2048 taps then you get a frequency resolution 0.73 Hz. Whereas in case of 96 kHz samplerate for the high frequencies you can use a filter with 1024 taps resulting in 93.75 Hz resolution (which seems to be enough).
      This is the strategy of multirate filters. 
      There are of course points to take care about. The downsampling requires additional brickwall filters, the frequency range has to be split by filters which may introduce additional group delays (Lyngdorf is a good example). In case of active speakers a speaker driver may cover several areas and thus need a higher samplerate again with less resolution at the lower frequencies (example TacT).
      2. Simply use the available processing power of modern CPUs or GPUs and apply a filter with many taps in a brute force method. The disadvantage: you need processing power. But it is available. So a filter with 64k is no problem at all. You can get the desired resolution for the low frequency range. You also have a micro detail resolution for the high frequency range BUT you are not forced to use it !! If you decide to apply a correction only below 300 Hz and thus use a straight frequency response above for the correction then you can do it. It does not harm if the straight line consists of frequency bins with 0.5 Hz distance.

      There is no lunch for free.
      Each version has advantages and disadvantages.

      But in a discussion we should talk about the real advantages and disadvantages. IMHO it is nonsense to damn the high resolution of long filters (by some killer phrases) because the resolution is not necessary in the high frequency range. Because you can use the high resolution (it can be very useful e.g. with steep crossovers or notch filters to cancel cone break-ups) or you can leave it. It is up to you.

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