In the real world, the electromagnetic field is a multi-dimensional time-varying real-valued function (volts/meter or newtons/coulomb). But in mathematical physics and signal processing, we often use complex-valued representations of the field, or of quantities derived from it, to facilitate our mathematics or make the signal processing more compact and efficient.

So throughout the CSP Blog I’ve focused almost exclusively on complex-valued signals and data. However, there is a considerable older literature that uses real-valued signals, such as The Literature [R1, R151]. You can use either real-valued or complex-valued signal representations and data, as you prefer, but there are advantages and disadvantages to each choice. Moreover, an author might not be perfectly clear about which one is used, especially when presenting a spectral correlation surface (as opposed to a sequence of equations, where things are often more clear).

An example is the following sequence of four surfaces taken from [R151]:

In this post, I show my own surfaces for real- and complex-valued representations of these common PSK signals. In a previous post, I explained mathematically how the complex-valued representation relates to the real-valued representation. In a future Signal Processing ToolKit post, I’ll go over all the steps involved in obtaining the complex-valued representation of a signal from a real-valued one.

Continue reading “Spectral Correlation and Cyclic Correlation Plots for Real-Valued Signals”