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I am a computer science student working on a school project involving RTL-SDR receivers, and I have a hard time grasping the concept of IQ data. Basically what I think I have learned from all of the videos I watched on the topic is that the I signal is the captured signal multiplied by some sine wave, while the Q signal is also the captured signal multiplied by cosine wave, thus making the signals 90 degrees out of phase from each other, and helping us determine if the captured signal was above or below our center frequency.

Now, this is where I get confused, because shouldn't that mean that I and Q signals are basically identical, just out of phase? I tried looking that up, and almost everywhere I looked people say that the signals are not the same and are completely different. Any help would be appreciated!

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The important takeaway is: using a radio, you can transmit two signals "at the same time" (technically: over the same bandwidth). One of the signals is known as I (in-phase), the other as Q (quadrature).

How is this possible? If you take signals $s_1(t)$ and $s(t)$ and transmit them "at the same time", the received signal is just $r(t) = s_1(t) + s_2(t)$, right? There's no way to determine $s_1(t)$ and $s_2(t)$ from $r(t)$.

Except radios transmit over the passband: the signals are "upconverted" before transmission. Upconversion means multiplying by a high-frequency sinusoid. The transmitted signal is actually $$s(t) = s_1(t)\cos(2\pi f_c t) + s_2(t)\sin(2\pi f_c t).$$

Remarkably, it is possible to "disentangle" $s(t)$ and recover $s_1(t)$ and $s_2(t)$.

I'll let you work out the math, but here's the final result:

$$ s_1(t) = \text{LPF}\lbrace s(t)\cos(2\pi f_c t) \rbrace$$

and

$$ s_2(t) = \text{LPF}\lbrace s(t)\sin(2\pi f_c t) \rbrace,$$

where $\text{LPF}$ is a low pass filter, basically a device that removes the high frequency terms that result from the multiplications above.

Note that a simple radio may use only the I signal, and set the Q signal to zero. This results in a simpler system that works perfectly fine, except that technically it is "wasting" half of the available resources.

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    $\begingroup$ The difficult part is making sure that the $\cos(2\pi f_c t)$ used in the receiver has the same frequency and phase as the $\cos(2\pi f_c t)$ in the transmitter. Same for the $\sin(2\pi f_c t)$. They must be synchronized or else your $s_1(t)$ and $s_2(t)$ will contaminate each other. $\endgroup$ Nov 25, 2023 at 20:33
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It might be best to compare an IQ signal with complex numbers, or circle on an XY plane, or phasors.

As the IQ signal is a sum of sine wave with some amplitude and cosine wave with some amplitude, the sum of those will also be a new sine wave with some new amplitude, but with a new phase offset compared to phases of original sine and cosine whose phase offset might have been assumed 0.

So instead of thinking you can send two signals, sine with amplitude and cosine with amplitude, you can think of sending a sine wave, with amplitude and phase.

That's a bit like a circle on a XY plane. You can point a coordinate on the circle with radius and angle, or you can point a coordinate on the circle with X and Y coordinates, and they relate through sine and cosine.

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In SDRs, multiplying a real-valued bandpass signal by a cosine wave, and simultaneously multiplying that real-valued bandpass signal by a sine wave, generates a complex-valued signal that has been frequency translated to be centered at zero Hz. Doing so makes it easier to perform AM and FM demodulation of the original real-valued bandpass signal.

Perhaps the material at the following web page will be of some value to you:

https://www.dsprelated.com/showarticle/192.php

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