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1. Don Romano (alt) (thor@noagendasocial.com)'s status on Wednesday, 17-Apr-2019 16:13:52 EDT Don Romano (alt)

   1) The problem I'm trying to solve essentially looks like this animation:

   https://images.app.goo.gl/iNf1XwxHFLRrZkLu6

   Given two sine waves with the same frequency but different phases and amplitudes (here represented as phasors), what is the peak amplitude of their sum across a 360 degree cycle?

   If my understanding of phasors is right, summing the two phasors on the complex plane at a given instant should produce a phasor that represents the sum of the actual waveforms.

   1. Don Romano (alt) (thor@noagendasocial.com)'s status on Wednesday, 17-Apr-2019 16:17:24 EDT Don Romano (alt)

      in reply to

      2) Now, if that's true, a rotation of the resulting phasor should behave as if the two phasors are rotating.

      Now, if that is true, the magnitude of this phasor should represent the maximum real magnitude of the summed waveforms, since it will hit that magnitude on the real plane whenever it intersects with the horizontal axis.

      1. Don Romano (alt) (thor@noagendasocial.com)'s status on Wednesday, 17-Apr-2019 16:47:10 EDT Don Romano (alt)

         in reply to

         3) So, the answer to "What is the amplitude of two summed sine waves of equal periods but different amplitudes and phases?" would seem to boil down to something like:

         v₁ = A₁ cos(ϕ₁) + A₂ cos(ϕ₂),
         v₂ = A₁ sin(ϕ₁) + A₂ sin(ϕ₂)

         M₁₂ = √v₁² + v₂²

         Essentially tacking one phase vector of a sine wave onto the end of another and finding the distance from the origin.

         Does this sound right?

         1. Don Romano (alt) (thor@noagendasocial.com)'s status on Wednesday, 17-Apr-2019 16:56:12 EDT Don Romano (alt)

            in reply to

            4) The purpose of this exercise is that I'm writing a simple microphone array simulator with the goal of producing polar patterns for whole arrays. I want to see what happens if you move microphones around or sum/subtract them in different ways, so I'm using ray-casting to each element from an orbiting source and naturally I need to know what happens to the amplitude as that's going on in order to render a polar pattern.

            1. Don Romano (alt) (thor@noagendasocial.com)'s status on Wednesday, 17-Apr-2019 17:02:14 EDT Don Romano (alt)

               in reply to

               5) Phasors are pretty awesome. FFT coefficients are also phasors. The output of an FFT is an array of phasors representing the amplitude and phase of sine waves at evenly spaced frequencies between DC and the Nyquist frequency. If you use a big FFT window and manipulate the phase angles while leaving the amplitudes intact, you can produce some really weird and wonderful audio smearing effects.