4-1. Design of the updated value \(α_i\) and \(δ_i\)

Using the update value \(α_i\) is for the CORDIC method, it is brought close to the angle \(θ \) to be obtained. Updated value is defined by \(δ_i\), as shown in (1.6) formula.The re-defined as follows when designing the hardware of the \(δ_i\).

To redefine also \(α_i\) using (4.1) this equation.

And to define the value in this way, faster computation is possible in the case of performing binary multiplication with \(δ_i\) in the conversion type, in addition to the representation can be easily fixed point, and using a shift operation is for. In the example circuit, for the construction of the circuit by the determination of the angle \(z \) which will be described later, a value in consideration of the point operations \(tan^(-1)\) is difficult in hardware, pre-calculated to (4.2) equation (4.1) wherein I stored in the ROM. In addition, both should be a positive value the value to be stored in the ROM.

Figure5：Design of the circuit of update value \(α_i\) and \(δ_i\)

i indicates the number of iterations, a value corresponding to the input i is output from the ROM.