The Art of the Helicopter John Watkinson - Karatunov.net

Technical background 47
Fig. 2.28 Fourier analysis allows the synthesis of any waveform by the addition of discrete frequencies of
appropriate amplitude and phase.
by creating all of the right harmonics and adding them is called an inverse transform.
Figure 2.29 shows how a square wave can be synthesized in this way by adding together
different harmonics of the correct amplitude and phase.
Fourier analysis is based on multiplying the waveform to be analysed by sine waves
called ‘basis functions’. In order to analyse an arbitrary waveform to see if it contains
a particular frequency, it is multiplied by a basis function at that frequency and the
product is averaged. Figure 2.30(a) shows that if the signal being analysed contains a
component having the same frequency as that of the basis function the product will have
a zero frequency component that will give a finite result after averaging. The value of
the result after averaging is called a coefficient. Components at all other frequencies will
average to zero. Thus a complete Fourier analysis requires the process to be repeated
at all of the frequencies of interest.
Figure 2.30(c) shows that if by chance the input and the basis function have a phase
difference of 90 ◦ the product will be zero even though the frequencies are identical.