Half-Bands are very flat in the passband, and somewhat efficient to implement because every second tap is zero. The CIC on the other hand, is super efficient, but has a horrible frequency response.
So, you want to use the half-bands for decimation whenever possible. You will have fewer aliases, the spectrum looks nicer, etc. More halfbands is always better. But two halfbands was chosen because on the N210, it's a good compromise between available resources and spectral improvements. Also, keep in mind that you can only stack halfbands as long as your decimation is a multiple of two. If your decimation is 6 (= 2 * 3), then you can only use one halfband, and set the CIC to 3. In other words, adding another halfband only enables rates where the decimation rate is a multiple of 8, and so on. Next, why are they different. That was another compromise. More taps are always better, so why not use the bigger one twice? That's because when cascading the halfbands, the fidelity of the second filter reduces the requirement for a super-good first filter. If you draw this on a piece of paper, it's more obvious, but here's an attempt at writing it as text: Fewer taps in a halfband mean the transition band (from passband to stop band) is wider, which makes the flat passband smaller. However, because the second half-band will further reduce the total available bandwidth, you don't need a super sharp transition zone. Finally, what does the multiplier do. In software, we calculate a total gain of our DSP chain, based on the CIC settings and some other numbers we have figured out. For example, the CORDIC has an almost constant, non-zero gain. and the CIC decimator has a non-constant gain which is a function of the decimation (all of this because we're doing fixpoint math). We try and negate this as much as possible by multiplying the output with a compensation factor. -- M On Fri, Oct 11, 2019 at 10:57 AM Francesco Restuccia via USRP-users < usrp-users@lists.ettus.com> wrote: > Dear all, > I have some questions regarding the DDC implementation (ddc_chain.v, > usrp2): > > 1) Why do we need two half-band filters (one large and one small) after > the CIC? What is their purpose? Can’t we use just one half-band? > 2) What is the purpose of the scale factor multiplication after hb2? What > does it compensate for? How do we decide its value? > > Thanks, > Francesco > _______________________________________________ > USRP-users mailing list > USRP-users@lists.ettus.com > http://lists.ettus.com/mailman/listinfo/usrp-users_lists.ettus.com >
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