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BC:8.1 A periodic signal with period To = known to have the form f(t) = Σ at exp k=-∞ 2π (12 kt) (jkt To 125 ns is where ao = -15, a1 = 12.54-13°, a -1 a2 = 327°, a -2 = 32-7°, and all other a = 0. = 12.5/13º, a.) What is the fundamental frequency (in Hz) for the periodic signal. b.) Use the Euler formula to express f(t) as the sum of cosines plus a constant.

BC:8.1 A periodic signal with period To = known to have the form f(t) = Σ at exp k=-∞ 2π (12 kt) (jkt To 125 ns is where ao = -15, a1 = 12.54-13°, a -1 a2 = 327°, a -2 = 32-7°, and all other a = 0. = 12.5/13º, a.) What is the fundamental frequency (in Hz) for the periodic signal. b.) Use the Euler formula to express f(t) as the sum of cosines plus a constant.

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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**BC:8.1** A periodic signal with period \( T_o = 125 \, \text{ns} \) is known to have the form: \[ f(t) = \sum_{k=-\infty}^{\infty} \alpha_k \exp \left( j \frac{2\pi}{T_o} kt \right) \] where \( \alpha_0 = -15 \), \( \alpha_1 = 12.5 \angle -13^\circ \), \( \alpha_{-1} = 12.5 \angle 13^\circ \), \( \alpha_2 = 3 \angle 7^\circ \), \( \alpha_{-2} = 3 \angle -7^\circ \), and all other \( \alpha_k = 0 \). a.) What is the fundamental frequency (in Hz) for the periodic signal? b.) Use the Euler formula to express \( f(t) \) as the sum of cosines plus a constant.
Transcribed Image Text:**BC:8.1** A periodic signal with period \( T_o = 125 \, \text{ns} \) is known to have the form: \[ f(t) = \sum_{k=-\infty}^{\infty} \alpha_k \exp \left( j \frac{2\pi}{T_o} kt \right) \] where \( \alpha_0 = -15 \), \( \alpha_1 = 12.5 \angle -13^\circ \), \( \alpha_{-1} = 12.5 \angle 13^\circ \), \( \alpha_2 = 3 \angle 7^\circ \), \( \alpha_{-2} = 3 \angle -7^\circ \), and all other \( \alpha_k = 0 \). a.) What is the fundamental frequency (in Hz) for the periodic signal? b.) Use the Euler formula to express \( f(t) \) as the sum of cosines plus a constant.
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