一個高精確度的固定頻寬布氏乘法器採用可調整的統計方法

A High-Accuracy Fixed-Width Booth Multiplier with Adaptive Statistical Algorithm

費聿亞(Yu-Ya Fei)

指導教授 ： 張慶元

國立清華大學/電機資訊學院/電機工程學系/碩士(2012年)

https://doi.org/10.6843/NTHU.2012.00709

摘要

在數位訊號處理系統中，乘法器是不可或缺的角色。但在有些數位訊號處理的應用上，乘法器的輸入以及輸出需要相同的位元數，如此就必須捨棄掉一部分的乘積結果，而這捨棄的部份進而影響到了乘法器的精準度，因此許多人致力於研究適當的補償方法，以提高此種乘法器的精準度。
本篇論文提出了一個可藉由統計範圍不同而改變其精準度的固定頻寬布氏乘法器。本文所提出的乘法器中的布氏演算法是採用radix-4的演算法去改良，將要捨去的部分乘積一部分先做了運算，且加上四捨五入的概念而得到一個新的真值表。在補償值方面，我們藉由統計部分乘積結果與布氏演算法的編碼結果找出其相互關係，進而推導出其補償公式。另外我們進一步藉由統計部分乘積的範圍再次探討與布氏編碼的關係，提出的適當的改良方法，最後導出與精準度參數和布氏編碼結果相關的補償公式。

關鍵字

錯誤補償 ； 固定頻寬乘法器 ； 改良式布氏演算法

並列摘要

Multiplier is an important component in the application of digital signal processing (DSP) systems. However, it is desirable to remain the same bit width for the multiplication in some applications. For this reason, fixed-width multipliers only keeps the most significant half part of the products and a large error would be produced. Thus, many compensation methods are provided to solve this problem.
In this research, an error compensation method with different statistical result for fixed-width Booth multiplier is produced. Booth algorithm in this research has been improved from radix-4 Booth algorithm. The modified Booth algorithm pre-calculated some of the partial products and combined the rounding, so that we can get a new true table with higher accuracy. About the compensation value, we want to find the relationship between the statistical result of the partial product and the result of the modified Booth algorithm. Furthermore, we statistic different range of the partial product and discuss the new problem about the relationship. Finally, a compensation function with different statistical result produced.

並列關鍵字

error compensation ； fixed-width multiplier ； modified Booth algorithm

參考文獻

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