Two Birds with One Tone: I/Q Signals and Fourier Transform

Summary

When a new member arrives at the Signal Processing Club, this is what they find at the club gate: I/Q signals. Perhaps a secret plot to keep most people out of the party? Some return from here to try another area (e.g., machine learning, which pays more and is easier to understand but less interesting than signal processing). Others persist enough to push the gate open for implementation purposes (even a little understanding is sufficient for this task) but never fully grasp the main idea. So what exactly makes this topic so mysterious? To investigate the answer, we start with an example audio signal drawn in the figure below that displays amplitude versus time for some spoken words. For a comparison, a radio signal with digital modulation is plotted below. Clearly, both audio and radio signals are simple real waveforms plotted with time. Why then I/Q processing is not common in traditional audio applications but an integral part of radio communications? For this purpose, Part 1 delves into the significance of I/Q processing in wireless systems, and Part 2 broadens the scope, linking the I/Q signals (also known as quadrature signals) to Fourier Transform, the most important tool in all signal processing applications. Let us start with the nature of an electromagnetic wave. An Electromagnetic Messenger Wireless systems employ an electromagnetic wave acting as a carrier of information hidden in the variations of its parameters. The Sinusoidal Wave This electromagnetic wave is produced by an oscillator through acceleration and deceleration of charges in the forward and reverse directions. Since the charges primarily oscillate back and forth, the wave exhibits a sinusoidal form. A reverse process occurs on the receive side. The impinging EM wave influences the electrons in the antenna through its electric and magnetic fields. The acceleration and deceleration of these electrons under the influence of these fields creates a tiny sinusoidal electrical signal. In signal pr...