Image frequency doubt about cosinusoidal/sinusoidal signals

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Image frequency doubt

in a mixer system, if the band of interest is located in ωRF=ωLO+ωIF, then its image is located in ωIM=ωLO-ωIF.
Both are frequency translated to the same IF because cos(ωLO+ωIF)=cos(ωLO-ωIF).
This is with cosenoidals input signals, but what about if using senoidal input functions ? sin(ωLO+ωIF)≠sin(ωLO-ωIF)
 

Re: Image frequency doubt

I think the problem here is that you're confusing time and frequency domains.
The upper and lower sidebands are at frequencies of wLO+wIF and wLO-wIF. This is the frequency domain; wLO+wIF is a frequency.

Now if, say, the LO and IF are both simple cosine waves, then the output will be 2 simple cosine waves: cos( (wLO+wIF)t) and cos( (wLO-wIF)t), ignoring any phase components and where t is time. This is the time domain; note the 't' in the argument. These are not the same waveforms in any way.

You are trying to evaluate sin( wLO+wIF), without the time parameter and it has no meaning in either domain. I'm not even sure why you declare that cos(wLO+wIF) = cos(wLO-wIF).

Hope this helps.
 

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