The Quantization Effects of CORDIC Arithmetic for Digital Signal Processing Applications

CORDIC (COordinate Rotation DIgital Computer) is an algorithm for performing a sequence of iteration computation using the coordinate rotation. It can generate some powerful elementary function only realized by a simple set of adder and shifter. As such, it is suitable to implement high performance chips, which are applied in digital signal processing and image processing fields with high speed and massive function computation using VLSI technology. In this paper, we discuss and analyze the computation error of the CORDIC algorithm. We analyze the CORDIC algorithm and categorize different types of computation error in order to derive from them systematically. Each type of error analysis includes rotation mode and vectoring mode according to characteristic of the CORDIC algorithm, and the computation error of each mode is made up of approximation error and truncation error. We have not only considered and promoted some neglected errors and formulas, but also revealed the outcomes of error analysis in the form, which is only related to the number of iteration and word length only. We also reveal the design reference with the error tolerance in tables.