Getting to Grips with Aircraft Noise
Getting to Grips with Aircraft Noise
Getting to Grips with Aircraft Noise
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Flight Operations Support & Line Assistance<br />
<strong>Getting</strong> <strong>to</strong> grips <strong>with</strong> aircraft noise<br />
9 - A BIT OF THEORY<br />
• More generally, any periodic sound signal can be split up in<strong>to</strong> FOURIER series<br />
(decomposition as the infinite sum of elementary pure sounds)<br />
∑ ∞<br />
p t)<br />
C n<br />
( = sin ( nωωωωt<br />
+ ϕϕϕϕ )<br />
0<br />
where : ωωωω corresponds <strong>to</strong> the fundamental pulsation<br />
nωωωω are the harmonics.<br />
Cn are the Fourier coefficients (amplitude of each elementary<br />
pure <strong>to</strong>ne)<br />
C n<br />
Fundamental<br />
• Practically, a sound is not periodic and thus cannot be split up in<strong>to</strong> a Fourier<br />
series. In that case, the frequency spectrum is continuous and the previously<br />
mentioned Fourier series become an integral called the Fourier transform.<br />
Then, any sound can be expressed thanks <strong>to</strong> the inverse Fourier transform<br />
(C(f) being the direct Fourier transform of p(t)), which makes the pair <strong>with</strong> the<br />
Fourier series when the signal period becomes infinite.<br />
∫ +∞<br />
−∞<br />
f 0 2f 0 3f 0 …<br />
jωt<br />
p(<br />
t)<br />
= C(<br />
f ) e df<br />
Harmonics<br />
Where: C(f) is called spectrum of the acoustic pressure p(t).<br />
f<br />
65
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