## Standards and Conventions

### Scope of Standards and Conventions

Phased Array System Toolbox™ software
uses consistent conventions with respect to units of measure, data
representations, and coordinate systems. You must understand these
conventions to use the toolbox.

### Complex-Valued Baseband Signals

In phased array signal processing, it is common to shift the
frequency content of a waveform to support effective radiation and
propagation in the medium. You accomplish this task by modulating
a baseband signal with nonzero spectral magnitudes in the vicinity
of zero frequency to create a bandpass signal with nonzero spectral
magnitudes centered around a carrier frequency. Typically, the bandwidth
of the baseband signal is small compared to the carrier frequency
resulting in a narrowband signal. To process returned signals, the
receiver demodulates the bandpass signal to the baseband. The demodulation
involves local oscillators both in phase and 90 degrees out of phase
with the modulating carrier frequency. This demodulation results in
in-phase (I) and quadrature (Q) baseband signals, or channels. For
processing, it is convenient to create a complex-valued baseband signal
by assigning the I channel to be the real part and the Q channel to
be the imaginary part, *I*+*jQ*.

This software uses the complex-valued baseband representation
to represent both transmitted and received signals. Actual phased
array systems transmit real-valued signals and create complex-valued
baseband signals only at the receiver. However, you can use a complex-valued
representation at all stages. Doing so enables you to accurately model
the effect of system gains, losses, and interference on the received
signal samples.

### Data Organization of Baseband Signals

You can use this software to efficiently implement space-time
processing of complex-valued baseband samples by organizing the data
in a three-dimensional matrix. See Radar Data Cube for an explanation of how the software organizes
space-time data.

### Spatial Coordinates

Representation of position in three dimensions is a fundamental
aspect of array signal processing. This software specifies rectangular
and spherical coordinates as column vectors with respect to both global
and local origins. For a detailed explanation of the conventions,
see:

### Physical Quantities

This software uses the International System of Units (SI) almost
exclusively for measurement. In addition, there are physical constants
declared and used in calculations. See Units of Measure and Physical Constants for a detailed explanation
of the conventions.

### Supported Data Types

This software supports only double-precision data types.