digequal - ECE 421 - Sum 2010 Notes Set 4: Digital...

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Unformatted text preview: ECE 421 - Sum 2010 Notes Set 4: Digital Equalizers 1 INTRODUCTION In the previous Notes Set we studied the Z-transform and some of its properites. In this set of Notes we expand our understanding of the Z-transform to show how it helps us solve some important problems in digital signal processing. The DSP structures which solve these problems are sometimes called Digital Equalizers and/or Inverse Filters. To motivate the study of these DSP structures in this set of Notes, let’s consider the following situations: ¯ In a high-speed digital communications system a stream of digital bits is sent through a channel to a receiver. Examples are DSL transmitting through the twisted-pair phone line or a wireless modem transmitting over a wireless local area network. However, due to the dispersive properties of the channel, the received signal is a distortion of the transmitted signal, even with no noise. Making “bit decisions” on this received data stream would lead to many errors. Therefore, we sometimes use a Digital Equalizer to remove the effects of the channel distortion before making a decision on the received bits. ¯ Geophysical seismology often involves transmitting a short acoustic pulse into the earth and then recording the returning acoustic reflections. The reflections are di- rectly related to the reflecting boundaries (like rock strata) within the earth. In this case, information is desired about these discrete reflecting boundaries, which can be modelled as impulses. However, since the returning acoustic reflections are a convo- lution on the transmitted pulse and the sequence of “boundary impulses”, the actual reflecting boundary positions are not obvious. Processing the returned reflection sig- nal with an Inverse Filter can be used to perform a deconvolution which can often isolate the position of the reflecting boundaries One approach to finding the DSP structures which solve the above problems uses the Z- domain to obtain the solutions. In this set of Notes we explore this approach and investigate some of the properties of the resulting equalizers and inverse filters. ECE 421 - Sum 2010 Notes Set 4: Digital Equalizers 2 DIGITAL EQUALIZER: Time-Domain In this Notes Set we will primarily study the digital equalizer. Let’s simplify the problem by assuming the channel impulse response h [ m ℄ is known. The corresponding digital model for the system which uses an equalizer is shown in the block diagram below: [ ] s m Channel E [ ] v m + [ ] h m [ ] h m [ ] y m [ ] r m All the signals in the above block diagram are digital baseband signals. In the block di- agram above, s [ m ℄ is the transmitted information signal, v [ m ℄ is the additive noise and/or interference, and r [ m ℄ is received signal. Mathematically we have r [ m ℄= h [ m ℄ ?...
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This note was uploaded on 09/07/2010 for the course ECE 421 taught by Professor Hallen during the Summer '08 term at N.C. State.

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digequal - ECE 421 - Sum 2010 Notes Set 4: Digital...

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