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And why, according to some sources, these filters have different number of taps (the last is the shortest one)? Does it really reduce a cost of computation?

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  • $\begingroup$ Yes, they are more efficient. $\endgroup$ – Arnfinn Dec 10 '16 at 2:10
  • $\begingroup$ But why? I'm trying to design this kind of filter chain. At every step I'm getting higher order or filter to maintain the same transition band width measured in Hz. $\endgroup$ – e_asphyx Dec 10 '16 at 3:27
  • $\begingroup$ The order and phase delay in the filter will be high, but the number of arithmetic operations needed in order to implement the filter will be greatly reduced. That is the improvement over a regular FIR filter. $\endgroup$ – Arnfinn Dec 10 '16 at 7:43
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The reason cascaded half-band filters, for interpolation applications, should have different numbers of taps can be found at: https://www.dsprelated.com/showarticle/903.php

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    $\begingroup$ Could you summarize the content at the link you provided? Stack Exchange usually tries to prevent link-only answers, lest the links die over time. $\endgroup$ – Jason R Dec 12 '16 at 1:45
  • $\begingroup$ @JasonR , totally agree with the policy on the link-only answers. $\endgroup$ – Gilles Dec 12 '16 at 8:09
  • $\begingroup$ @JasonR. Ah, OK. I understand. I could give no truly meaningful answer to e_asphyx's sensible question in just a few sentences here. As it turns out, I wrote a blog, with complete text and several figures, dedicated to e_asphyx's exact question! At the link I posted he can download a PDF of my blog to keep for the rest of his life. $\endgroup$ – Richard Lyons Dec 13 '16 at 9:21

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