Abstract
This paper proposes a novel multiplierless comb compensation filter, which has the absolute passband deviation less than 0.1 dB in the wide passband. The compensator consists of a cascade of two simple filter sections, both operating at a low rate. The magnitude characteristics of the two-component filters are synthesized as sinewave functions, in which the main design parameters correspond to the amplitudes of sinewave functions. A systematic procedure is followed to select synthesis parameters, which depend only on the number of cascaded comb filters. In particular, they are independent of the decimation factor. Comparisons with comb compensators from the literature illustrate the benefits of the proposed design.
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This work was supported by CONACYT Grant Nos. 179587 and 264138.
Appendix
Appendix
Here, the derivation of (29) is presented in detail.
From (27), we have:
Using (14), we write:
where \(\omega _{k}\) are arbitrary frequencies in the passband, given by
Placing (32) into (31), we get:
From (3), we write by noting that the comb magnitude response is positive in the passband:
We rewrite (35) as:
Placing (33) into (36), we get:
Similarly, using (4), we write:
From (34), (37), and (38), we arrive at:
From here, we have:
Also,
and
Using (5), we write:
where values \(B_{1}\) are given in Table 2.
Finally, from (42) and (43), we arrive at:
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Jovanovic Dolecek, G., Baez, R.G., Molina Salgado, G. et al. Novel Multiplierless Wideband Comb Compensator with High Compensation Capability. Circuits Syst Signal Process 36, 2031–2049 (2017). https://doi.org/10.1007/s00034-016-0398-0
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DOI: https://doi.org/10.1007/s00034-016-0398-0