8 Recall that we derived the following Fourier pair in class.\[\cos(\omega_0 t) \xleftrightarrow{\text{FT}} \pi \left( \delta(\omega - \omega_0) + \delta(\omega + \omega_0) \right).\]**(Part a)** Derive the FT of \( x_1(t) = \cos^2(\omega_0 t) \).**(Part b)** Let \( m(t) \xleftrightarrow{\text{FT}} M(j\omega) \) be defined as in the sketch below, where \( \angle M(j\omega) = 0 \):**Diagram:**- The plot of \( M(j\omega) \) is a semicircular arc above the \(\omega\)-axis.- The arc is centered at the origin and extends from \(-10\pi\) to \(10\pi\) on the \(\omega\)-axis.- The peak magnitude of the arc is 1 at \(\omega = 0\).Sketch the FT of \( x_2(t) = m(t) \cos(40\pi t) \).**(Part c)** Sketch the FT of \( x_3(t) = x_2(t) \cos(40\pi t) \).

Answered: Image /qna-images/answer/60dd65b8-5ccc-444e-9b10-b4ddb50872ba.jpg

Recall that we derived the following Fourier pair in class. FT cos(wot) + → π (8 (w — wo) + 8(w + wo)). (Part a) Derive the FT of x₁(t) = cos² (wot). FT (Part b) Let m(t) ← → M(jw) be defined as in the sketch below, where LM (jw) = 0: -10π 1 M(jw) Sketch the FT of x₂(t) = m(t) cos(40πt). (Part c) Sketch the FT of x3(t) = x₂(t) cos(40πt). 10π ω

Recall that we derived the following Fourier pair in class. FT cos(wot) + → π (8 (w — wo) + 8(w + wo)). (Part a) Derive the FT of x₁(t) = cos² (wot). FT (Part b) Let m(t) ← → M(jw) be defined as in the sketch below, where LM (jw) = 0: -10π 1 M(jw) Sketch the FT of x₂(t) = m(t) cos(40πt). (Part c) Sketch the FT of x3(t) = x₂(t) cos(40πt). 10π ω

Introductory Circuit Analysis (13th Edition)

13th Edition

ISBN:9780133923605

Author:Robert L. Boylestad

Publisher:Robert L. Boylestad

Chapter1: Introduction

Section: Chapter Questions

Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...

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