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2. The signal x(t) can be expressed as the sum of two signals; x1(t) and x2(t); x(t)=x1(t)+x2(t) where, x1 (t) = { -1sts1 ,and otherwise -1 +1 +2 t(s) -1sts2 x,(t) = 0 Fig. 1 %3D otherwise (a) Find the CTFT of x1(t) using Fourier Pairs (use the table) (b) Find the CTFT of x2(t) using Fourier Pairs and Fourier properties (time-shift) (c) Find the CTFT of x(t0 by adding the results of (a) and (b): X(@) = X,(w) +X2(w)

2. The signal x(t) can be expressed as the sum of two signals; x1(t) and x2(t); x(t)=x1(t)+x2(t) where, x1 (t) = { -1sts1 ,and otherwise -1 +1 +2 t(s) -1sts2 x,(t) = 0 Fig. 1 %3D otherwise (a) Find the CTFT of x1(t) using Fourier Pairs (use the table) (b) Find the CTFT of x2(t) using Fourier Pairs and Fourier properties (time-shift) (c) Find the CTFT of x(t0 by adding the results of (a) and (b): X(@) = X,(w) +X2(w)

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
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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I need help solving calculation part 2. Please include descriptions of each step
Objectives: 1. Determine the Fourier transform of a CT signal using Integration form 2. Determine the Fourier transform of a CT signal using Fourier transform pairs and its properties 3. Plot the magnitude and phase spectra of a CT signal I. CALCULATION PART 1. Using integration form of Fourier transform, compute the CTFT for the CT signal x(t) in Fig. 1 x(t) 8. X (@) = x(t)e-jutdt -00 2. The signal x(t) can be expressed as the sum of two signals; x1(t) and x2(t); x(t)=x1(t)+x2(t) where, x, (t) = {6 -1 st<1 and otherwise' -1 +1 +2 t(s) (1 -1 <t< 2 x2(t) = t0 Fig. 1 otherwise (a) Find the CTFT of x1(t) using Fourier Pairs (use the table) (b) Find the CTFT of x2(t) using Fourier Pairs and Fourier properties (time-shift) (c) Find the CTFT of x(t0 by adding the results of (a) and (b): X(@) = X,(@) + X2(@) 3. Find the magnitude A(w) and phase (w) spectra of x(t) and determine their values in Table 1 and Table 2 Table 1 T/8 T/4 Зп/8 Tt/2 5t/8 би /8 7TT/8 A(@) $(@) Table 2 -/8 -T/4-3T/8 -T/2 |-5T/8 -61/8 -71/8 A(@) $(w)
Transcribed Image Text:Objectives: 1. Determine the Fourier transform of a CT signal using Integration form 2. Determine the Fourier transform of a CT signal using Fourier transform pairs and its properties 3. Plot the magnitude and phase spectra of a CT signal I. CALCULATION PART 1. Using integration form of Fourier transform, compute the CTFT for the CT signal x(t) in Fig. 1 x(t) 8. X (@) = x(t)e-jutdt -00 2. The signal x(t) can be expressed as the sum of two signals; x1(t) and x2(t); x(t)=x1(t)+x2(t) where, x, (t) = {6 -1 st<1 and otherwise' -1 +1 +2 t(s) (1 -1 <t< 2 x2(t) = t0 Fig. 1 otherwise (a) Find the CTFT of x1(t) using Fourier Pairs (use the table) (b) Find the CTFT of x2(t) using Fourier Pairs and Fourier properties (time-shift) (c) Find the CTFT of x(t0 by adding the results of (a) and (b): X(@) = X,(@) + X2(@) 3. Find the magnitude A(w) and phase (w) spectra of x(t) and determine their values in Table 1 and Table 2 Table 1 T/8 T/4 Зп/8 Tt/2 5t/8 би /8 7TT/8 A(@) $(@) Table 2 -/8 -T/4-3T/8 -T/2 |-5T/8 -61/8 -71/8 A(@) $(w)
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