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Two Birds with One Tone: I/Q Signals and Fourier Transform
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
user-generated (e.g., wireless communications), arising from the laws of nature (e.g., radar, astronomy, remote sensing, biomedical), or both (e.g., navigation and positioning systems, beamforming). In bygone times, messages were delivered either by homing pigeons traveling long distances or by spies arriving on horseback at the gates of a walled city. At the Tx side, the $I$ and $Q$ amplitude streams can be seen as two parallel wires before they are mixed with respective sinusoids and summed together to form a single signal $x(t)$ of Eq (\ref{equation-iq}) that is sent into the air.
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