Speech and Audio Signal Processing: Processing and Perception of Speech and Music, Second Edition

PART II

MATHEMATICAL BACKGROUND

Baseball is 90% mental. The other half is physical.

–Yogi Berra

IT IS not possible to understand speech and audio signal processing in any depth without having a solid background in the mathematical underpinnings of signal processing and pattern recognition. There are many good books on these topics, and this text is not intended to replace them. However, in Part II we have gathered together some major points and concepts that we feel the reader must grasp. While distributing earlier drafts of this text, we found that the backgrounds of interested students and colleagues varied greatly. Therefore, even though we have limited the discussion to a few principal relevant points, we have included material at several levels of difficulty. A very brief introduction into the most relevant engineering mathematics for signal processing and pattern recognition is provided here. Readers who have studied this material previously may still wish to refresh their memories, or at least touch on familiar material lightly in order to get the feeling for our style of notation. Some advanced sections are also provided, such as the discussion of the Expectation-Maximization algorithm in Chapter 9.

Chapters 6 and 7 focus on digital signal processing, and Chapters 8 and ...