TAILIEUCHUNG - Digital communication receivers P9

Timing Adjustment by Interpolation In this chapter we focus on digital interpolation and interpolator control. In Section we discuss approximations to the ideal interpolator. We first consider FIR filters which approximate the ideal interpolator in the mean square sense. A particularly appealing solution for high rate applications will be obtained if the dependency of each filter tap coefficient on the fractional delay is approximated by a polynomial in the fractional delay. It is shown that with low-order polynomials excellent approximations are possible. In Section we focus on how to determine the basepoint m, and fractional delay Pi, considering. | Digital Communication Receivers Synchronization Channel Estimation and Signal Processing Heinrich Meyr Marc Moeneclaey Stefan A. Fechtel Copyright 1998 John Wiley Sons Inc. Print ISBN 0-471-50275-8 Online ISBN 0-471-20057-3 Chapter 9 Timing Adjustment by Interpolation In this chapter we focus on digital interpolation and interpolator control. In Section we discuss approximations to the ideal interpolator. We first consider FIR filters which approximate the ideal interpolator in the mean square sense. A particularly appealing solution for high rate applications will be obtained if the dependency of each filter tap coefficient on the fractional delay is approximated by a polynomial in the fractional delay. It is shown that with low-order polynomials excellent approximations are possible. In Section we focus on how to determine the basepoint mn and fractional delay considering either a timing error feedback system or a timing estimator. Digital Interpolation The task of the interpolator is to compute intermediate values between signal samples x kTs . The ideal linear interpolator has a frequency response Section -L S s J a n oo x z 9-1 with i w zT3 exPÜ w w 2tt 1 2T s tO elsewhere 9-2 and is shown in Figure 9-1. iœT. IH e 8 n l 1 1 J 1 I I 1 1 1 1 -3k - 2k k i q k 2k 3k oT8 Figure 9-1 Frequency Response of the Ideal Interpolator 505 506 Timing Adjustment by Interpolation Figure 9-2 Impulse Response of the Ideal Interpolator The corresponding impulse response Figure 9-2 is the sampled si ar function hi nTs j Ts si - nTs zT3 9-3 Conceptually the filter can be thought of as an FIR filter with an infinite number of taps hn ji hi nTSi j T3 si - nTs Ta n . -1 0 1 . 9-4 Digital Interpolation 507 x mk 1 Ts x mkTs x mk-1 Ts Figure 9-3 FIR Filter Structure of the Ideal Interpolator The taps are a function of 1. For a practical receiver the interpolator must be approximated by a finite-order FIR filter 3 9-5 n -h In Figures 9-3 and 9-4 the FIR filter .

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