magnitude Archives

In this post, let us discuss a simple implementation friendly scheme for computing the absolute value of a complex number $Z = X+jY$ . The technique called $\alpha Max + \beta Min$ (alpha Max + beta Min) algorithm is discussed in Chapter 13.2 of Understanding Digital Signal Processing, Richard Lyons and is also available online at Digital Signal Processing Tricks – High-speed vector magnitude approximation

The magnitude of a complex number $Z = X+jY$ is

$|Z| = \sqrt{X^2 + Y^2}$ .

The simplified computation of the absolute value is

$|Z| \approx \alpha Max + \beta Min$ where

$Max = \max \left( |X|, |Y| \right)$

$Min = \min \left( |X|, |Y| \right)$ .

Continue reading “Approximate Vector Magnitude Computation”

In a previous post (here), we looked at using CORDIC (Co-ordinate Rotation by DIgital Computer) for understanding how a complex number $\mathbf{X}$ can be rotated by an angle $\theta$ without using actual multipliers. Let us know try to understand how we can use CORDIC for finding the phase and magnitude of a complex number.

Basics

The CORDIC algorithm is built on successively multiplying the complex number $\mathbf{X}$ , by $\mathbf{Y} =1 + j2^{-k}$ . As can be noticed, as the elements of $\mathbf{Y}$ can be represented in powers of 2, the multiplication can be achieved by using the appropriate ‘bit shift’. For further details, please refer to the previous post (CORDIC for phase rotation).

Continue reading “Using CORDIC for phase and magnitude computation”