The quantization effects of the CORDIC algorithm

Author

Hu, Yu Hen

Author_Institution

Dept. of Electr. & Comput. Eng., Wisconsin Univ., Madison, WI, USA

Volume

40

Issue

4

fYear

1992

fDate

4/1/1992 12:00:00 AM

Firstpage

834

Lastpage

844

Abstract

A detailed analysis of the quantization error encountered in the CORDIC (coordinate rotation digital computer) algorithm is presented. Two types of quantization error are examined: an approximation error due to the quantized representation of rotation angles, and a rounding error due to the finite precision representation in both fixed-point and floating-point arithmetic. Tight error bounds for these two types of error are derived. The rounding error due to a scaling (normalization) operation in the CORDIC algorithm is also discussed. An expression for overall quantization error is derived, and several simulation examples are presented

Keywords

computerised signal processing; digital arithmetic; iterative methods; roundoff errors; CORDIC algorithm; approximation error; coordinate rotation digital computer; error bounds; fixed point arithmetic; floating-point arithmetic; iterative arithmetic algorithm; normalization; quantization error; rounding error; scaling; signal processing; simulation; Algorithm design and analysis; Computer errors; Digital arithmetic; Iterative algorithms; Process design; Quantization; Roundoff errors; Signal processing algorithms; Vectors; Very large scale integration;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.127956

Filename

127956