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Scope of Standards and Conventions Complex-Valued Baseband Signals |

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.

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.

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.

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:

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.

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