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let me explain it : The transfer of signals occupying a specified frequency band, such as a channel or group of channels, from one portion of the frequency spectrum to another, in such a way that the arithmetic frequency difference of signals within the band is unaltered. One key operation is the frequency translation of a signal spectrum from one center frequency to another. Conversions between baseband and bandpass representations (modulation and demodulation) are special cases of this. Conceptually, the most simple case is the (complex) I/Q-mixing. Here the input sequence is multiplied by a complex exponential signal corresponding to the local oscillator (LO) frequency fLO.
(2.1)
It follows directly from the properties of Fourier transform that I/Q mixing causes a pure frequency translation of the signal spectrum:
(2.2)
Complex mixing used to produce pure frequency translation of input spectrum.
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