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Gordana Jovanovic Dolecek (Institute INAOE Puebla, Mexico)

Copyright: © 2018
|Pages: 14

DOI: 10.4018/978-1-5225-2255-3.ch525

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TopThe transfer function of comb filter is given by the following equation:

The magnitude response of the filter is given as:

The comb pass band is defined by the pass band edge (Kwentus &Willson, 1997):

For values *R*<4, the pass band is considered as a wideband, and in an opposite case it is a narrowband.

As an example, Figure 1 shows the wide pass band zoom (*R*=2), of the magnitude response of comb filter with the decimation factor *M*=12 and an order equal to *K*=3. Note that the response is not flat and has a droop, which increases with the increase of the frequency *ω*. The inverse comb magnitude characteristic:

The product of the magnitude characteristics (2) and (4) results in unity:

Consequently, in order to get a flat comb magnitude characteristic it is necessary to cascade comb with a filter which has magnitude characteristic approximately equal to the inverse comb magnitude characteristic in the pass band. This filter is called a compensation filter. Denoting the magnitude characteristic of compensator as it follows:, for 0 ≤*ω*≤ *ω _{p}*

Usually, compensation filter works at a low rate, i.e. after decimation. As a consequence, at high input rate, compensator is expanded by *M*.

The compensated comb is the cascade of comb and compensator. The corresponding transfer function at high input rate is:

Multiplierless Design: The coefficients of filter are presented as powers of two which can be implemented as shifts and adders, thus avoiding multipliers.

Comb Filter: A simplest decimation filter which has all coefficients equal to unity.

Comb Compensation Filter (Compensator): The filter which has the magnitude characteristic which is an approximation of the inverse comb magnitude characteristic in the pass band. The filter is cascaded with the comb filter.

Comb Passband: The frequency band in which the decimated signal must be preserved. Ideally its characteristic is inverse of that of comb, thus resulting in approximately flat magnitude characteristic of the compensated comb in the pass band. The width of the pass band depends on the comb decimation factor, and the decimation factor of the stage which follows the comb decimation stage.

Error Function: The difference of the desired and designed magnitude responses of compensated filter.

Multipliers: Implementation of coefficients of filter transfer function which cannot be presented as a power of two.

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