Cordic in MATLAB

Let’s z be a 2D point in the space as \(z = x + jy\), if we want to rotate this point a given angle \(\theta\), we get the following expressions:
\[e^{j\theta} \cdot z = \left(\cos{\theta} + j \sin{\theta}\right)\left(x+jy\right) \\ = x\cos{\theta}-y\sin{\theta} + j \left(y \cos{\theta} + x \sin{\theta} \right) \\ = x’ + j y’ \]

Then, for a generic point, the rotation can be expressed as an equation system, where \(x’\) and \(y’\) are the new coordinates, \(\theta\) is the rotation angle and \(x\) and \(y\) are the original coordinates:
\[\begin{bmatrix}
x’\\
y’
\end{bmatrix}=
\begin{bmatrix}
\cos{\theta} & -\sin{\theta}\\
\sin{\theta} & \cos{\theta}
\end{bmatrix}\begin{bmatrix}
x\\
y
\end{bmatrix} \]

This rotation can be coded in MATLAB as:

A possible implementation of the cordic algorithm could be:

 

I have coded an interactive applet to illustrate the algorithm. It has been done using the p5.js library. The error limit has been set to \(0.5\).

Rubén Sánchez Mínguez
IC design engineer en Analog Devices

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