1.2. Core Algorithms
For signal processing problems requiring the detection of a signal and estimation of its parameters, there exist some statistically sound and consequently, well accepted approaches. As examples, we mention the matched filter for detection, the maximum likelihood estimator and its frequent implementation, the least squares estimator, for parameter estimation. It is these well accepted approaches that we intend to focus on. Hopefully, with exposure to the techniques that work in practice, the signal processing algorithm designer will at least have a good starting point from which to proceed to an actual design. Many of the core approaches, in addition to more advanced but possibly not proven-in-practice techniques, have been described in detail in the first two volumes of Fundamentals of Statistical Signal Processing [Kay 1993, Kay 1998] and in Modern Spectral Estimation: Theory and Application [Kay 1988]. The latter book on spectral analysis is important for modeling of random signals and provides many useful algorithms for computer generation of these signals. The reader is encouraged to refer to these books for a fuller understanding of the theoretical underpinnings of these approaches. In this volume we
- Describe the important algorithms used in practice,
- Describe the assumptions required for their successful operation, and
- Describe their performance and their limitations in practice.
This book is an attempt to accomplish these goals without having had the exposure to the books referenced above.