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Problem Statement: Open with The given signal x{t), is the continuous time input to an LTI system, i.e., System 1. The impulse response of the LTI system (System 1) is given as h, (t). The output signal y,t) is the convolved output. As shown in the block diagram (figure 1), the output y,(t) is input to two other functional blocks, i.e., the Fourier Series (FS) block and the Truncation Function block. The FS block converts this time domain signal into frequency domain signal by providing the magnitude and phase spectra at its output. The truncation function block converts this periodic signal into aperiodic signal by truncating the signal for t>T ,which becomes the input to second LTI System (System 2). The impulse response of this LTI system is given as h,t) . The convolved output of System 2 is given as y,t). Fourier transform is applied at y,t) to identify the frequency components along its magnitude and phase spectra. Determine, a. Step by step Convolved output y,le). b. Frequency coefficient of Fourier series, magnitude and phase spectra at output 1. c. Step by step Convolved output y, t). d. Frequency coefficient of Fourier transform, magnitude and phase spectra at output 2. h;(t), LTI System 2 x(t) LTI System 1 Y¼(t) Truncation →V½(t) Function F.S F.T www. Output 1 Output 2

Problem Statement: Open with The given signal x{t), is the continuous time input to an LTI system, i.e., System 1. The impulse response of the LTI system (System 1) is given as h, (t). The output signal y,t) is the convolved output. As shown in the block diagram (figure 1), the output y,(t) is input to two other functional blocks, i.e., the Fourier Series (FS) block and the Truncation Function block. The FS block converts this time domain signal into frequency domain signal by providing the magnitude and phase spectra at its output. The truncation function block converts this periodic signal into aperiodic signal by truncating the signal for t>T ,which becomes the input to second LTI System (System 2). The impulse response of this LTI system is given as h,t) . The convolved output of System 2 is given as y,t). Fourier transform is applied at y,t) to identify the frequency components along its magnitude and phase spectra. Determine, a. Step by step Convolved output y,le). b. Frequency coefficient of Fourier series, magnitude and phase spectra at output 1. c. Step by step Convolved output y, t). d. Frequency coefficient of Fourier transform, magnitude and phase spectra at output 2. h;(t), LTI System 2 x(t) LTI System 1 Y¼(t) Truncation →V½(t) Function F.S F.T www. Output 1 Output 2

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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Please Solve part 'a' only.

Problem Statement: Open with The given signal x(t), is the continuous time input to an LTI system, i.e., System 1. The impulse response of the LTI system (System 1) is given as h, (t) . The output signal y,lt) is the convolved output. As shown in the block diagram (figure 1), the output y, t) is input to two other functional blocks, i.e., the Fourier Series (FS) block and the Truncation Function block. The FS block converts this time domain signal into frequency domain signal by providing the magnitude and phase spectra at its output. The truncation function block converts this periodic signal into aperiodic signal by truncating the signal for t>T ,which becomes the input to second LTI System (System 2). The impulse response of this LTI system is given as h, t) . The convolved output of System 2 is given as y, t). Fourier transform is applied at y2t) to identify the frequency components along its magnitude and phase spectra. Determine, a. Step by step Convolved output y, t). b. Frequency coefficient of Fourier series, magnitude and phase spectra at output 1. c. Step by step Convolved output y,t). d. Frequency coefficient of Fourier transform, magnitude and phase spectra at output 2. h2(t). LTI System 2 x(t) LTI System 1 Truncation Yı(t) +y2(t) Function F.S F.T Output 1 Output 2
Transcribed Image Text:Problem Statement: Open with The given signal x(t), is the continuous time input to an LTI system, i.e., System 1. The impulse response of the LTI system (System 1) is given as h, (t) . The output signal y,lt) is the convolved output. As shown in the block diagram (figure 1), the output y, t) is input to two other functional blocks, i.e., the Fourier Series (FS) block and the Truncation Function block. The FS block converts this time domain signal into frequency domain signal by providing the magnitude and phase spectra at its output. The truncation function block converts this periodic signal into aperiodic signal by truncating the signal for t>T ,which becomes the input to second LTI System (System 2). The impulse response of this LTI system is given as h, t) . The convolved output of System 2 is given as y, t). Fourier transform is applied at y2t) to identify the frequency components along its magnitude and phase spectra. Determine, a. Step by step Convolved output y, t). b. Frequency coefficient of Fourier series, magnitude and phase spectra at output 1. c. Step by step Convolved output y,t). d. Frequency coefficient of Fourier transform, magnitude and phase spectra at output 2. h2(t). LTI System 2 x(t) LTI System 1 Truncation Yı(t) +y2(t) Function F.S F.T Output 1 Output 2
x(t) in. 1 2T 3T 4T 5T t h:(t) 1- T 2T h2(t) 1 T
Transcribed Image Text:x(t) in. 1 2T 3T 4T 5T t h:(t) 1- T 2T h2(t) 1 T
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