# Calculate Min/Max value of multiple sine waves added together

So I feel like this should be possible, I'm just not sure how to do it. Let's say I'm generating a signal with a sample rate of 10K samples/second. Then let's say my signal is comprised of X number of frequencies( we'll use 3 for this example). For each sample I want to take the three frequencies and add them together, lets use 1000Hz, 1250Hz, and 1500Hz. Now that i've added them together, they might be too large (lets say the max value i can output is a 1) so then i need to normalize them. Is there a way to calculate the maximum or minimum value that these three frequencies will produce over a given period of time/number of samples so that i can get normalize my signal accordingly?

Thanks for any input on this!

• If the sine waves are all harmonically related, the relative starting phases will affect the maxima peak. – hotpaw2 Aug 21 '15 at 23:13

• For a half/double frequency with a phase shift for the individual components this is not true, e.g., $s_1(n) = \sin(2\pi f_0/f_s n)$ and $s_2(n) = \sin(4\pi f_0/f_s n + \pi/2)$. However, summing the invidual magnitudes provides an upper limit. – Brian Aug 22 '15 at 12:04