Addition of different frequency sinosoids

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Faizan Tahir Butt

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how to add sinosoids of different frequency and amplitude?
 

Faizan Tahir Butt,
In the analog world this is easily accomplished by use of a simple op-amp summing circuit.
.
In the digital world it is accomplished by simple addition, either in hardware or in software.
Regards,
Kral
 

we want to solve mathematically and graphically on paper! please reply.
 

I'm also interested in understanding this. I want to find the beat frequency and wave frequency after the addition.

The only idea that i have now is to use the product and sum formula--

cos(a)+cos(b)=2cos((a+b)/2)cos((a-b)/2)
 

product and sum formula are not applicable when amplitudes are different.
 

add elements of same time index
 

Faizan Tahir Butt said:
product and sum formula are not applicable when amplitudes are different.
Click to expand...

To understand the effects, writing,
cos(f1)+1.7*cos(f2)=cos(f1)+cos(f2)+0.7*cos(f2)
may help

Has many limitations (analysis of more than 3 frequency components etc.). If you get a better method, please post it here.
 

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