Section 18.5 Parseval's Theorem

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Section 18.5 Parseval’s Theorem

18.52 For

$$F(\omega) = \frac{3}{3 + j\omega}$$

, find $J = \int_{-\infty}^{\infty} f^2(t) dt$ .

18.53 If

$$f(t) = e^{-2|t|}$$

, find $J = \int_{-\infty}^{\infty} |F(\omega)|^2 d\omega$ .

• 18.54 Design a problem to help other students better understand finding the total energy in a given signal.
• 18.55 Let f (t) = 5e⁻(t−2)u(t). Find F(ω) and use it to find the total energy in f(t).
• 18.56 The voltage across a 1-Ω resistor is v(t) = te⁻2*^t u*(t) V. (a) What is the total energy absorbed by the resistor? (b) What fraction of this energy absorbed is in the frequency band −2 ≤ ω≤ 2?
• 18.57 Let i(t) = 2et u(−t) A. Find the total energy carried by i(t) and the percentage of the 1-Ω energy in the frequency range of −5 < ω< 5 rad/s.