Question

Gow to calculate peak value of sum of more than 2 cosine signal

Answer 1

Let's define:

f(t)=A1cos(ω1t)+A2cos(ω2t)

I am interested in finding an expression for the peak of this function. It is not true in general that this peak will have the value:

maxf(t)=A21+A22+2A1A2−−−−−−−−−−−−−−√

To find the value of max(f), I did the following manipulations:

ω2=ω1+Δω1

so I can express the second cosine as that of a sum of a single radian frequency:

f(t)=A1cos(ω1t)+A2cos(ω1t+Δωt)

and after a little algebra:

f(t)=[A1+A2cos(Δωt)]cos(ω1t)−A2sin(Δωt)sin(ω1t)