1 Answer. Sorted by: 10. It is just a matter of manipulating complex numbers. ∠ H ( ω) = tan − 1 ( ℑ { H ( ω) } ℜ { H ( ω) }) Where ℜ { ⋅ } is the real part and ℑ { ⋅ } is the imaginary part. (NOTE: this

Phase Shift of Sinusoidal Functions The general sinusoidal function is: f ( x) = ± a ⋅ sin ( b ( x + c)) + d The constant c controls the phase shift. Phase shift is the horizontal shift left or right for periodic functions. If c = π 2

phase shift = −0.5 (or 0.5 to the right) vertical shift D = 3 In words: the 2 tells us it will be 2 times taller than usual, so Amplitude = 2 the usual period is 2 π, but in our case that is sped up (made shorter) by the 4 in 4x, so Period = π/2 and the

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