Fixed-Point Signal Processing (Paperback)

This book is intended to fill the gap between the "ideal precision" digital signal processing (DSP) that is widely taught, and the limited precision implementation skills that are commonly required in fixed-point processors and field programmable gate arrays (FPGAs). These skills are often neglected at the university level, particularly for undergraduates. We have attempted to create a resource both for a DSP elective course and for the practicing engineer with a need to understand fixed-point implementation. Although we assume a background in DSP, Chapter 2 contains a review of basic theory and Chapter 3 reviews random processes to support the noise model of quantization error. Chapter 4 details the binary arithmetic that underlies fixed-point processors and then introduces fractional format for binary numbers. Chapter 5 covers the noise model for quantization error and the effects of coefficient quantization in filters. Because of the numerical sensitivity of IIR filters, they are used extensively as an example system in both Chapters 5 and 6. Fortunately, the principles of dealing with limited precision can be applied to a wide variety of numerically sensitive systems, not just IIR filters. Chapter 6 discusses the problems of product roundoff error and various methods of scaling to avoid overflow. Chapter 7 discusses limit cycle effects and a few common methods for minimizing them. There are a number of simple exercises integrated into the text to allow you to test your understanding. Answers to the exercises are included in the footnotes.

本書旨在填補數位信號處理（DSP）中「理想精確度」與固定點處理器和現場可程式閘陣列（FPGA）常見的有限精確度實現技巧之間的差距。這些技巧在大學階段通常被忽略，尤其是對於本科生而言。我們試圖創建一個資源，既適用於DSP選修課程，也適用於需要理解固定點實現的實踐工程師。雖然我們假設讀者具備DSP背景，但第2章對基本理論進行了回顧，第3章則回顧了隨機過程，以支持量化誤差的噪聲模型。第4章詳細介紹了固定點處理器的二進制算術，並引入了二進制數字的小數格式。第5章涵蓋了量化誤差的噪聲模型以及濾波器中係數量化的影響。由於IIR濾波器的數值敏感性，它們在第5章和第6章中被廣泛用作示例系統。幸運的是，處理有限精確度的原則可以應用於各種數值敏感的系統，而不僅僅是IIR濾波器。第6章討論了乘積截斷誤差的問題以及避免溢出的各種縮放方法。第7章討論了極限循環效應以及一些常見的最小化方法。書中融入了一些簡單的練習題，供讀者測試理解程度。練習題的答案包含在腳註中。