Capitolul 1: Semnale
Capitolul 1: Semnale
Capitolul 1: Semnale
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Spectru ideal de joasă frecvenţă (2)<br />
• Def. Funcţia sinc (nucleul Dirichlet) este<br />
sincω = sinω<br />
ω .<br />
• Folosind transformata Fourier inversă obţinem<br />
x[n] = 1<br />
2π<br />
∫ π<br />
−π<br />
= sin(ω tn)<br />
πn<br />
X(ω)e jωn dω = 1<br />
2π<br />
= ω t<br />
π sinc(ω tn).<br />
∫ ωt<br />
−ω t<br />
e jωn dω = 1<br />
2πjn ejωn ∣ ∣∣∣<br />
ω t<br />
−ω t<br />
• Am obţinut deci egalitatea<br />
X(ω) =<br />
∞∑<br />
n=−∞<br />
sin(ω t n)<br />
e −jωn = ω t<br />
πn π<br />
∞∑<br />
n=−∞<br />
sinc(ω t n)e −jωn .<br />
PS cap. 1: <strong>Semnale</strong> – p. 22/43
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