99280_contoh Soal Signal Dan Basic Signal - 2.docx
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1.7 Show that the complex exponential signal
Persamaan Euler: 𝑒 𝑗𝜔0𝑇 = 1 cos 𝜔0 𝑇 + 𝑗 sin 𝜔0 𝑇 = 1. Agar persamaan ini dipenuhi, maka bagaian imajiner 𝑗 sin 𝜔0 𝑇 = 0, shg cos 𝜔0 𝑇 = 1. Agar cos 𝜔0 𝑇 = 1 dan sin 𝜔0 𝑇 = 0, maka 𝜔0 𝑇 = 0, 2𝜋, 4𝜋, 6𝜋, ...dst, sehingga 𝜔0 𝑇 = 𝑚 2𝜋, dengan m = bilangan integer bernilai positif. Jadi, 𝑇 = 𝑚
2𝜋 𝜔0
Catatan: Cos(A+B) = cos A cos B – sin A sin B, dengan 𝐴 = 𝜔0 𝑡 + 𝜃 dan 𝐵 = 𝜔0 𝑇 Agar sisi kanan = sisi kiri (agar dipenuhi syarat keperiodikan), maka cos B = 1 dan sin B = 0
Persamaan Euler: 𝑒 𝑗𝜔0𝑇 = 1 cos 𝜔0 𝑇 + 𝑗 sin 𝜔0 𝑇 = 1. Agar persamaan ini dipenuhi, maka bagaian imajiner 𝑗 sin 𝜔0 𝑇 = 0, shg cos 𝜔0 𝑇 = 1. Agar cos 𝜔0 𝑇 = 1 dan sin 𝜔0 𝑇 = 0, maka 𝜔0 𝑇 = 0, 2𝜋, 4𝜋, 6𝜋, ...dst, sehingga 𝜔0 𝑇 = 𝑚 2𝜋, dengan m = bilangan integer bernilai positif. Jadi, 𝑇 = 𝑚
2𝜋 𝜔0
Catatan: Cos(A+B) = cos A cos B – sin A sin B, dengan 𝐴 = 𝜔0 𝑡 + 𝜃 dan 𝐵 = 𝜔0 𝑇 Agar sisi kanan = sisi kiri (agar dipenuhi syarat keperiodikan), maka cos B = 1 dan sin B = 0
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