eklhad@ihnet.UUCP (K. A. Dahlke) (01/18/86)
Given the amplitudes of the first N harmonics of a wave form (A[1] ... A[N]), determine the phase angles that will minimize the maximum value of the composite wave. In other words, the wave form F is the sum of A[i] * cos(theta[i] + i*x). Find values for theta[i] that minimize the range of F. The worst case is quite easy. When all phase angles are 0, F(0) is the sum of the component amplitudes. The range just couldn't get any higher. Finding the best case (lowest bound for F) is more difficult. This problem actually has an application. A friend of mine is generating music by storing the wave form for a note digitally. He wants to keep memory consumption down to a dull roar, therefore, he wants to restrict the range of F, thus restricting the number of bits required to represent each sample. On the other hand, he wants the individual harmonic components to have relatively high amplitudes, since this improves the signal to noise ratio. Apparently, he can phase shift harmonics with impunity, since humans do not perceive phase angles. Of course, non harmonic components are generated elsewhere. Well, anyways, this is math, not computers. Can anyone help us find a procedure for computing optimal phase angles, given the amplitudes of the first N harmonics? -- Why don't we do it in the road? Karl Dahlke ihnp4!ihnet!eklhad