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Up/Down Mixing is the translation of the signal centred at some frequency to a higher/lower frequency. This is normally done by multiplying it with a signal of a controlled frequency and then filtering the output. This is used in any wireless receiver where the signal has to be shifted in frequency to the base band. Example is a Superhetrodyne receiver.
for example consider a signal of frequency f, multiply it with let us take simple example cos(ω1t)
we will get two frequencies in the output f+f1(up) and f-f1 (down). Likewise we can go any range of frequencies, this is what used in SSB modulation in AM signals and also by doing so we can transmit the same signal in any number frequencies to a single receiver.
incertain commn. systems, modulation process needed to be done at lower level(ie low carrier freq.... high freq.carrier generation leads to instability) after doing modulation at low frequency itself,that modualted carrier will be multiplied by constant or mixed with some frequency to form sum & diiference frequency. here comes device called as mixer...whose output is summation and difference of given input frequencies.
Mixing is especially used to convert Narrowband to wideband FM conversion.
as well in SSBSC generation(filter method)....