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Real-Time Digital Signal Processing - Chapter 8: Adaptive Filtering

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As discussed in previous chapters, filtering refers to the linear process designed to alter the spectral content of an input signal in a specified manner. In Chapters 5 and 6, we introduced techniques for designing and implementing FIR and IIR filters for given specifications. Conventional FIR and IIR filters are time-invariant. They perform linear operations on an input signal to generate an output signal based on the fixed coefficients. | Real-Time Digital Signal Processing. Sen M Kuo Bob H Lee Copyright 2001 John Wiley Sons Ltd ISBNs 0-470-84137-0 Hardback 0-470-84534-1 Electronic 8 Adaptive Filtering As discussed in previous chapters filtering refers to the linear process designed to alter the spectral content of an input signal in a specified manner. In Chapters 5 and 6 we introduced techniques for designing and implementing FIR and IIR filters for given specifications. Conventional FIR and HR filters are time-invariant. They perform linear operations on an input signal to generate an output signal based on the fixed coefficients. Adaptive filters are time varying filter characteristics such as bandwidth and frequency response change with time. Thus the filter coefficients cannot be determined when the filter is implemented. The coefficients of the adaptive filter are adjusted automatically by an adaplive algorithm based on incoming signals. This has the important effect of enabling adaptive filters to be applied in areas where the exact filtering operation required is unknown or is non-stationary. In Section 8.1 we will review the concepts of random processes that are useful in the development and analysis of various adaptive algorithms. The most popular least-mean-square LMS algorithm will be introduced in Section 8.2. Its important properties will be analyzed in Section 8.3. Two widely used modified adaptive algorithms the normalized and leaky LMS algorithms will be introduced in Scdion 8.4. In this chaptcr. we introduce and analyze the LMS algorithm following the derivation and analysis given in 8 . In Section 8.5 we will briefly introduce stm c important applications of aclapti ve filtering. The implementation considerations will be discussed in Section 8.6 and the DSP implementations using the TMS320C55x will be presented in Section 8.7. 8.1 Introduction to Random Processes A signal is called a deterministic signal if it can be described precisely and tie rcprod ucccl exactly and .