COnfusion About Complex Signals
I am new to RF Design and I was introduced to the concept of complex signals and filters. But I cannot seem to understand the concept as to how do we have a complex signal in the real world.
For example when we multiply a real signal with a complex signal like exp(jωt) we are multiply the signal's spectrum with just a delta at frequecy ω and thus the entire spectrum just shifts to the right by ω as opposed to both right and left shifting if we multiply it with a real signla like a sine or a cosine. So how do we get the complex signal in the real world.
I found out that a book by Jan Crols Wireless CMOS Transceiver Design talks about this, but I cannot seem to find it anywhere.
If somebody can explain the concept to me or give me links or material where I can clarify this, it would be really helpful.
In the real world a complex signal is two orthogonal signals. There are some instrument that can generate complex signal. Here is one article. May it help you.
Best Regards
For example,
If you would like to transmit a signal like A+jB.
You just need to transmit a Acos(wt) + Bsin(wt)
that's becasue cos and sin are orthogonal.
No "j" in real world but you can use orthorgonal signal
to achieve it.
Ok, but still the main source of my confusion is, that like if we multiply a real signal with a complex signal like exp(jωt) (which is cosωt + j sinωt) we are multiplying the signal's spectrum with just a delta at frequecy ω and thus the entire spectrum just shifts to the RIGHT by ω.
But now consider multiplying the real signal by a sinωt and a cosωt separately. This will give us 2 spectrums which on magnitude addition give us a spectrum which is equivalent to LEFT shifting of the signal's spectrum !
I don't understand this discrepancy.
Another thing is that in such a structure where we multiply a signal by a sinωt and cosωt separately, we can freely take either sinωt or cosωt as the real part and hence more possibilities...
What does all this mean?