Vaisala RVP900 - 7 Processing Algorithms; RVP Algorithm Overview

7. Processing Algorithms
7.1 RVP Algorithm Overview
For information on dual polarization processing algorithms, see IRIS and RDA Dual
Polarization User Guide.
The discussion on processing algorithms implemented within the RVP900 signal processor
is confined to the mathematical description of these algorithms.
It is often convenient to combine two simultaneous samples of I and Q into a single complex
number (called a phaser) of the form:
s = I + jQ
where j is the square root of -1.
Most of the algorithms presented here are
defined in terms of the operations performed on
the s's, rather than the I and Q's. The use of the complex terms leads to a more concise
mathematical expression of the signal processing techniques being used.
During operation, the complex arithmetic is broken down into its real-valued component
parts in order to be computed by RVP900. For example, the complex product:
s = W × Y
is computed as:
Real{s} = Real{W} Real{Y} - Imag{W} Imag{Y}
Imag{s} = Real{W} Imag{Y} + Imag{W}Real{Y}
where Real{} and Imag{} represent the real and imaginary parts of their complex-valued
argument. Note that all of the expanded computations are themselves real-valued.
In addition to the usual operations of addition, subtraction, division, and multiplication of
complex numbers, we use three additional operators: ||, Arg and *. Given a number s in
the complex plane, the magnitude (or modulus) of s is equal to the length of the vector
joining the origin with s, that is by Pythagoras:

= Re  
2
+  
2
The signed (CCW positive) angle made between the positive real axis and the above vector
is:
Chapter 7 – Processing Algorithms
169