A/D Conversion Applications

We begin our excursion into the field of data conversion by reviewing the most frequently applied conversion principles. The next section explains the fundamentals of delta-sigma modulation. This paves the way for the section which provides a case study of a delta-sigma based high-resolution ADC system intended for a sonar application. This design example not only illustrates the various trade-offs on the architectural level but also addresses practical implementation issues on the physical level. Finally, the last section summarizes our findings and contains some concluding remarks.

Efficient Multirate Filtering

Application of multirate techniques to improve digital filter design and implementation are considered in this chapter. FIR and IIR filter design and implementation for sampling rate conversion by integer and rational factors are presented. Sharp narrow-band and wide-band multirate design techniques are discussed. Accurate designs of FIR and IIR half-band filters are described in detail. Several examples are provided to illustrate the multirate approach to filter design.

Introduction to Multirate Systems

This chapter treats the fundamentals of multirate system theory and includes decimation and interpolation as the basic concepts behind the changing of the sampling rate. The conversion of the sampling rate by an integer as well as by a rational number is explained. Also discussed are some widely used interconnections of upsamplers and downsamplers.

Wavelet Transforms and Multirate Filtering

One of the most fascinating developments in the field of multirate signal processing has been the establishment of its link to the discrete wavelet transform. Indeed, it is precisely this link that has been responsible for the rapid application of wavelets in fields such as image compression. The objective of this chapter is to provide an overview of the wavelet transform and develop its link to multirate filtering. The birth of the field of wavelet transforms is now attributed to the seminal paper by Grossman and Morlet (1984) detailing the continuous wavelet transform or CWT. The CWT of a square integrable function is obtained by integrating it over regions defined by translations and dilations of a windowing function called the mother wavelet. The idea of representing functions or signals in terms of dilations can be found even in engineering articles dating back by several years, for example, Helstrom (1966). However, Grossman and Morlet’s formulation was more complete and was motivated by potential application to modeling seismic data. The next step of significance was the discovery of orthogonal wavelet basis functions and their role in defining multi-resolution representations (Daubechies 1988; Meyer 1992). Daubechies also provided a method for constructing compactly supported wavelets. Mallat (1989) established the fact that coefficients of orthogonal wavelet expansions can be obtained through multirate filtering which paved the way for widespread investigation of using wavelet transforms in signal and image processing applications. The objective of the chapter is to provide an overview of the relationship between multirate filtering and wavelet transformation. We begin with a brief account of the CWT, then go through the discrete wavelet transformation (DWT) followed by derivation of the relationship between the DWT and multirate filtering. The chapter concludes with an account of selected applications in digital image processing.

Design and Implementation of Multirate Digital Filters

In this chapter we discuss techniques to design and implement multirate digital filters with low power consumption which also allow a reduction in the design effort, since the resulting circuits are highly modular and regular and can relatively easily be incorporated in the normal design flow of commercial tools. First we briefly review techniques that can be applied at various design levels, i.e., from algorithm level down to layout, to reduce the power consumption in CMOS implementations of both digital FIR and IIR filters and are useful in many other DSP algorithms. Second, we discuss the properties of lattice wave digital filters and various techniques to design efficient multirate digital filters for changing the sampling rate by a factor of two. Third, we discuss the design of multistage multirate digital FIR filter structures for arbitrary bandwidths. Finally, we provide some design examples.

Subband Coding of Signals

In this chapter we deal with subband coding of signals. We begin with an introduction to rate-distortion theory, and after that we discuss subband compression schemes in general. We then describe popular still image and video coding algorithms using subband decompositions, including DCT and wavelet-based methods. R-D optimization-based techniques such as wavelet packets are also described. We finish the chapter with a brief account of subband-based audio compression schemes.

Multirate Systems and Filterbanks

During the last two decades, multirate filter banks have found various applications in many different areas, such as speech coding, scrambling, adaptive signal processing, image compression, signal and image processing applications as well as transmission of several signals through the same channel (Malvar, 1992a; Vaidyanathan, 1993; Vetterli and Kovacevic, 1995; Fliege, 1994; Misiti, Misiti, Oppenheim and Poggi, 1996). The main idea of using multirate filter banks is the ability of the system to separate in the frequency domain the signal under consideration into two or more signals or to compose two or more different signals into a single signal.

Applications of Filter Banks to Communications

Multirate systems and filter banks have found many applications in source and channel coding over the last decade. This chapter addresses the design of multirate transceivers for optimal transmissions, blind channel identification and equalization, as well as the estimation of time-variant channels and channel statistics. It is hoped that the chapter illustrates how multirate systems and filter banks provide a bridge between communication system design/analysis and signal processing tools.

Speech and Audio Signal Applications

This chapter reviews the basic principles of multirate adaptive filters together with some of their most successful applications, as well as some recently proposed schemes that improve the subband adaptive signal processing systems.