Abstract

Abstract This paper mathematically investigates a special kind of digital infinite-impulse response (IIR) filters, suitable for filtering out very low frequencies near zero from digital signals. We investigate the transfer functions of such filters from 1st to 3rd order and provide formulas to calculate the filter coefficients from the desired cutoff frequency.

Highlights

  • Digital filtering plays a very important role in many data processing systems

  • This paper mathematically investigates a special kind of digital infinite-impulse response (IIR) filters, suitable for filtering out very low frequencies near zero from digital signals

  • This paper investigates a special kind of digital DC blocker filters

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Summary

Introduction

Sometimes it is necessary to remove a time-invariant additive offset from a signal [1, 2]. Such signal components are often named “DC offset”, the respective filter “DC blocker” (DC = “Directed Current” in contrast to “Alternating Current” = AC). M=0 n=1 where the xk−m are the input samples, yk−n the output samples, and the bm and an are constant real coefficients. Their values determine the characteristics of the filter, i.e., the spectral shaping of the signal when it passes the filter. For investigating the spectral properties, we perform a Fourier transform (in the following we only show important final results, for more details consult a textbook like [4,5,6])

Digital filter basics
First order
DC blocker filters
Second order
Third order
Low-pass filters
Calculating filter coefficients
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