Doubts of two scientists...

Last week I finally solved my satellite signal processing problem (with the help of my dear colleague). As I posted a few weeks ago, we are setting up a tracking station for satellites with some students here at the TUDelft. We record the signal coming from satellites and try to extract the frequency and frequency shift of that signal. Using the Doppler effect we can make an educated guess of where the satellites are and how fast they orbit the Earth (which is super-awesome!).

However, back to the problem. We record the signal in .wav format. This file consists of two channels, which both represent a signal as a time-serie with deviations from zero (when plotted it looks like a wavy pattern). However, there are two channels and at first I only used one of the two channels (I know now this is wrong, but hé, it was my first time dealing with this). In my first blog-post I showed a figure of the signal, however this figure was made by professional (wel, I think) open-source software. As a true Delft-engineer, I wanted to do it myself, just because I can. When I performed a Fourier transformation on the signal (one channel), I thought I got the correct result:

Time runs from up to down and the frequency bandwidth is shown on the horizontal axis. The signal was sort of mirrored around the center frequency (this was not a case of satellite synchronized swimming). I did something wrong, but me not being a signal processing expert, I could not understand what I did wrong. The best thing to do in such a case, is to leave the project alone (or go to the toilet with a cup of coffee, but I already tried that several times). 

After a few weeks, the problem was running around in my brain, screaming to be solved. Fortunately, my colleague needed to work with the Fourier transform (He is doing two-way laser ranging for interplanetary satellite missions, its kinda cool!!!). He asked me if he could use my data to see if his software is doing the correct thing. He got the same results as me, when he used only channel one of the .wav file. 

He, being a bit more (but also not an expert) known in the topic about electromagnetic radiation, came with the note that radio waves are complex. The radiation oscillates in the electric and magnetic field, creating a complex wave (A good figure is seen at, where else, wikipedia page). So he came up with the idea to make the second channel of the .wav file the imaginary part (just multiply the signal with the square root of -1, "Is this possible?", yes, it is.) of the complex signal and add it to the signal of the first channel. 

After doing the Fourier transform on the new and complex data (after zooming in on the signal), we got a beautiful figure of the Doppler shift in the carrier frequency of the satellite:

We'd extracted the same figure as the professional software did. I did a victory dance, for about two second, before I went back to work. But this is where my doubts started.

What was recorded on the .wav file? Is it the actual complex wave from the satellite, stating the trajectory of the energy package? Or is it a complex signal that could represent the signal best measured by the antenna, only stating the electric component of the signal, and therefore it is possible to see at both sides of the center frequency? This is where my knowledge stops about electromagnetic radiation. But I will try to find out what is really happening, because that is what science is about...