How is the phase angle computed?
Basically, the phase angle is the angle that you get when you compute the arc tangent of the ratio of the imaginary part to the real part of the complex spectrum at a particular frequency. However, beyond computing the arc tangent, you must do some additional work to take the quadrant into account. How should we interpret the phase angle? To begin with, you should ignore the result of phase angle computations at those frequencies for which there is insignificant energy. It is always possible to form a ratio of the values of the real and imaginary parts of the complex Fourier transform at any frequency. However, if the real and imaginary values produced by the Fourier transform at that frequency are both very small, the phase angle resulting from that ratio is of no practical significance. In fact, the angle can be corrupted by arithmetic errors resulting from performing arithmetic on very small values. Therefore, noting the amplitude spectrum in the second plot of Figure 2, phase angle
