# Meaning of Q and I in all-software QPSK communication systems?

Q and I seem to come up a lot in discussions of digital communications, such as the comprehensive answer provided to this question:

FFT window phase syncronising

It seems like the Q and I channels ultimately are combined into a sin wave of a given frequency, phase and amplitude. If the communications system is all software (for example in a software-defined radio) is it necessary to worry about "Q" and "I"? Is this just an artifact of when receivers and transmitters were electronics based?

To make the question more concrete, the link provided talks about putting the even bits onto Q and the odd bits onto I. If this is the same thing as creating a sin wave of phase 0, 90, 180, or 270, then why bother with this seemingly unnecessary notation? Perhaps the pulse shaping (like an RRC filter) needs to be independently applied to the Q and I channels?

• Consider looking at this question and this one and then thinking about why the unnecessary notation might be needed at least when analyzing the performance instead of just writing a few lines of Java code or whatever in your software radio. – Dilip Sarwate Jan 30 '13 at 15:35
• Look into QAM, how data is encoded into a "constellation" and then detected as an expected point in a"constellation". The constellation is a 2D map of amplitude and phase that is most understandable if you decompose your signal into I and Q components. The I and Q components form a vector that maps to a symbol in the constellation. – user2718 Jan 30 '13 at 16:12
• @Dilip: I did a lot of reading (including those questions) before asking. I understand that using complex numbers greatly simplify analysis. I've edited the question slightly -- I'd like to know if practically (when writing code) for QPSK you need to deal with the separate channels. Incidentally, I've found your many posts very valuable -- thank you. – Dan Sandberg Jan 30 '13 at 18:06
• @DanSandberg: The answer is yes. I and Q typically map to the real and imaginary components in a complex signal model. QPSK is a two-dimensional modulation scheme, so you definitely need both components. – Jason R Jan 30 '13 at 18:16

$$s_+(t)=s(t)+j \cdot \hat{s}(t) \; \; with \; \; \hat{s}(t)=\frac{s(t)}{\pi t}$$