# I and Q Channels

My understanding of I and Q channels is as follows (please correct me if I am wrong):

• I = In-phase, or real component
• Q = Quadrature (90° shift of real component)

Where do these two channels come from in the first place? Is one the electric field and the other the magnetic field of a EM wave? I was under the impression that these channels are only present in digital waveforms; if this is true, and if so, why?

How can this be used to find the vector of on incoming signal, and would the signal modulation make a difference (assuming you can invoke the proper filtering necessary)?

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I am not at all very knowledgeable of RF and signal processing concepts, so please forgive me if my questions, tags, etc. are not accurate. – Biff Jan 23 '13 at 23:56
You may want to check out this site. – Aaron D. Marasco Jan 24 '13 at 2:26
Thanks @AaronD.Marasco, I will check it out. – Biff Jan 24 '13 at 2:32
I just wanted to comment, but don't have that privilege yet. The top answer here gives a simple and clear explanation of how to obtain complex samples from real samples. Getting real samples from a real signal (analog) is fairly straightforward as long as Nyquist is heeded. – Dave C Jan 24 '13 at 21:20

## 1 Answer

The two channels exist only inside a transmitter or a receiver; the channels are physically combined in a single signal (or channel) in the physical medium (wire, coax cable, free space, etc). At the transmitter, two signals $s_I(t)$ and $s_Q(t)$ (called the I (or inphase) signal and Q (or quadrature) signal respectively) are combined into a single signal $s(t)$ that is transmitted over the physical medium in a frequency band centered at $\omega_c$ radians per second. Note that $$s(t) = s_I(t)\cos(\omega_c t) - s_Q(t)\sin(\omega_c t)$$ The receiver separates out the two signals $s_I(t)$ and $s_Q(t)$ from this by multiplying $s(t)$ by $2\cos(\omega_c t)$ and $-2\sin(\omega_c t)$ respectively, and low-pass filtering the two products. That is, \begin{align*} s_I(t) &= \text{result of low-pass filtering of}~ 2s(t)\cos(\omega_c t)\\ s_Q(t) &= \text{result of low-pass filtering of}~ -2s(t)\sin(\omega_c t) \end{align*} Note that \begin{align*} 2s(t)\cos(\omega_c t) &= 2s_I(t)\cos^2(\omega_c t) - 2s_Q(t)\sin(\omega_ct)\cos(\omega_c t)\\ &= s_I(t) + \bigr [s_I(t)\cos(2\omega_c t) - s_Q(t)\sin(2\omega_c t)\bigr]\\ -2s(t)\sin(\omega_c t) &= -2s_I(t)\cos(\omega_c t)\sin(\omega_c t) + 2s_Q(t)\sin^2(\omega_ct)\\ &= s_Q(t) + \bigr [-s_Q(t)\cos(2\omega_c t) - s_I(t)\sin(2\omega_c t)\bigr]\\ \end{align*} where the quantities in square brackets are double-frequency terms that are eliminated by the low-pass filtering.

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Does this mean that vector direction can be inferred from IQ modulation? Also, based on your explanation, it would seem that I & Q channels are present for any type of modulation? This begs the question: can vector direction be inferred from any type of modulated signal? – Biff Jan 24 '13 at 0:51
What do you mean by "vector direction?" – Jason R Jan 24 '13 at 2:19
Would it be possible to determine the magnitude (i.e. presumably the signal strength) of an oncoming signal and the direction oriented from its source? For example, if you were to move circularly around the receiving antenna (of which it may be dependent?), it would detect the corresponding change in direction. My expectation is that, because of the fundamental basis of the Fourier series, filtering could be used to identify the I & Q channels of any modulated signal and then calculate the oncoming vector magnitude and direction. – Biff Jan 24 '13 at 2:24
You're thinking of a "direction finding" technique. While that sort of thing is possible, it's a much more complex topic than this question on simple I/Q representation of signals. – Jason R Jan 24 '13 at 14:57
You are right. I'll do some research and think on the RDF technique more. – Biff Jan 25 '13 at 0:35