#フーリエ変換の具体的な計算 2

#矩形(くけい)関数を
rect(x) ＝
1　(－1≦x≦1)
0　(それ以外)
で定義。

#sinc(シンク)関数を
sinc(x) ＝ (sin x) / x
で定義。

この時
ℱ[ rect(t) ] ＝ 2 sinc(ω)
が成り立つ。

#矩形関数 を #フーリエ変換 すると
#sinc関数 になる！

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#デジタル信号とサンプリング 37

y(t)＝y_d(t) * sinc( ω_0･t )
(ω_0=π/τ)
を変形し

y(t)＝Σ{k=-∞→∞} y(kτ) sinc(ω_0･t － kπ) ★

★の意味:
「#サンプリング 値を
#sinc で重みづけしながら総和をとれば，
サンプリングしなかった
いかなる時刻の原信号の値も復元できる！」

#フーリエ変換の具体的な計算 2

#矩形(くけい)関数を
rect(x) ＝
1　(－1≦x≦1)
0　(それ以外)
で定義。

#sinc(シンク)関数を
sinc(x) ＝ (sin x) / x
で定義。

この時
ℱ[ rect(t) ] ＝ 2 sinc(ω)
が成り立つ。

#矩形関数 を #フーリエ変換 すると
#sinc関数 になる！

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