Editing Baseband (section)

=== Equivalent baseband signal ===
[[File:IQ Mod Demod block diagram.svg|thumb|right|400px|On the left is a part of the transmitter, which will take in a stream of baseband [[IQ data]], and use this to amplitude modulate a Local Oscillator's signal, both the standard sine wave from the LO, and also a version which phase shifted by 90° (in-phase and quadrature) - these modulated signals are combined, to form the [[Intermediate frequency]] IF representation.  In a typical transmitter, the IF would get up-converted, filtered, amplified, then transmitted from an antenna. (These are not shown)<br />On the right we see an aspect of the receiver.  After some low-noise amplification, filtering and down-conversion (not shown) to an IF, the signal is mixed with the in-phase sine from the LO, and also the quadrature version of the LO, giving a complex (or 2-dimensional) representation of the signal.  This [[IQ data]] could then be supplied to a [[digital signal processor]] to extract symbols or data.]]

An ''equivalent baseband signal'' or ''equivalent lowpass signal'' is a complex valued representation of the modulated physical signal (the so-called [[passband]] signal or [[radio frequency|RF]] signal). It is a concept within analog and digital modulation methods for (passband) signals with constant or varying [[carrier frequency]] (for example [[Amplitude-shift keying|ASK]], [[Phase-shift keying|PSK]] [[Quadrature amplitude modulation|QAM]], and [[Frequency-shift keying|FSK]]).  The equivalent baseband signal is <math>Z(t)=I(t)+jQ(t)\,</math> where <math>I(t)</math> is the inphase signal, <math>Q(t)</math> the quadrature phase signal, and <math>j</math> the [[imaginary unit]]. This signal is sometimes called ''[[IQ data]]''.  In a digital modulation method, the <math>I(t)</math> and <math>Q(t)</math> signals of each modulation symbol are evident from the [[constellation diagram]]. The frequency spectrum of this signal includes negative as well as positive frequencies. The physical passband signal corresponds to 
:<math>I(t)\cos(\omega t) - Q(t)\sin(\omega t) = \mathrm{Re}\{Z(t)e^{j\omega t}\}\,</math>
where <math>\omega</math> is the carrier [[angular frequency]] in rad/s.<ref name=Proakis>Proakis, John G. ''Digital Communications'', 4th edition. McGraw-Hill, 2001. p150</ref>