User's Manual

Processing Algorithms
RVP8 User’s Manual
March 2006
5–1
5. Processing Algorithms
Note: Optional dual polarization processing algorithms are described in Appendix B.
This chapter describes the processing algorithms implemented within the RVP8 signal processor.
The discussion is confined to the mathematical description of these algorithms. Figure 5–1
shows the overall process by which the RVP8 converts the IF signal into corrected reflectivity,
velocity, and width. Table 5–1 summarizes the quantities that are measured and computed by the
RVP8. The type of the quantity (i.e., real or complex) is also given. Subscripts are sometimes
used to denote successive samples in time from a given range bin. For example, s
n
denotes the
“I” and “Q” time series or “video” sample from the n’th pulse from a given range bin. In cases
where it is obvious, the subscripts denoting the pulse (time) are dropped. The descriptions of all
the data processing algorithms are phrased in terms of the operations performed on data from a
single range bin- identical processing then being applied to all of the selected ranges. Thus, there
is no need to include a range subscript in this data notation.
It is frequently 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 in this chapter are defined in
terms of the operations performed on the “s”’s, rather than the “I”’s and “Q”’s. The use of the
complex terms leads to a more concise mathematical expression of the signal processing
techniques being used. In actual operation, the complex arithmetic is simply broken down into
its real-valued component parts in order to be computed by the RVP8 hardware. 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 employ three additional unary 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”, i.e. by Pythagoras:
| s | + Real
{
s
}
2
) Imag
{
s
}
2
Ǹ
The signed (CCW positive) angle made between the positive real axis and the above vector is:
ë+Arg
{
s
}
+ arctan
ƪ
Imag
{
s
}
Real
{
s
}
ƫ