Addition of different frequency sinosoids

[Faizan Tahir Butt]

how to add sinosoids of different frequency and amplitude?

 

[Kral]

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

 

[Faizan Tahir Butt]

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

 

[nitrojacob]

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)

 

[Faizan Tahir Butt]

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

 

[xulfee]

add elements of same time index

 

[nitrojacob]

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

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.