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A signal, y(t), is described by the equation: (i) y(t) = where to 20 is a positive constant, and it means the magnitude of t. (ii) [A, if to -7/2<|t| ≤ to +7/2 0, otherwise Carefully plot the signal, y(t), paying attention to the region when y(t) is non-zero, and labelling all axes. Calculate the Fourier transform of the signal, y(t), denoted by Y (w).

A signal, y(t), is described by the equation: (i) y(t) = where to 20 is a positive constant, and it means the magnitude of t. (ii) [A, if to -7/2<|t| ≤ to +7/2 0, otherwise Carefully plot the signal, y(t), paying attention to the region when y(t) is non-zero, and labelling all axes. Calculate the Fourier transform of the signal, y(t), denoted by Y (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
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A rectangular pulse, x(t), of width 7 as shown overleaf in Figure B1, is defined by: t< −7/2 if-1/2 ≤ t < 7/2 a) The Fourier transform of the signal, x(t), is denoted by X (w) and expressed as: sin (w) w/7/2 (i) x(t) = (ii) A signal, y(t), is described by the equation: (iii) X (W) = AT (iv) 0, A, 0, t≥ ¹/2 y(t) = = AT sinc where to ≥ 0 is a positive constant, and |t| means the magnitude of t. (~7) SA, if to 7/2<|t| ≤ to + ¹/2 0. otherwise Carefully plot the signal, y(t), paying attention to the region when y(t) is non-zero, and labelling all axes. Calculate the Fourier transform of the signal, y(t), denoted by Y (w). Clearly show all your steps and working, but note that marks are awarded for concise approaches rather than a verbose long-winded solution. Provide an alternative derivation to calculate Y (w), different to your method in part a)(ii), and using further properties of the Fourier transform not already used. = Simplify your answer for the case to check if this solution is correct. T/2, and explain how you can
Transcribed Image Text:A rectangular pulse, x(t), of width 7 as shown overleaf in Figure B1, is defined by: t< −7/2 if-1/2 ≤ t < 7/2 a) The Fourier transform of the signal, x(t), is denoted by X (w) and expressed as: sin (w) w/7/2 (i) x(t) = (ii) A signal, y(t), is described by the equation: (iii) X (W) = AT (iv) 0, A, 0, t≥ ¹/2 y(t) = = AT sinc where to ≥ 0 is a positive constant, and |t| means the magnitude of t. (~7) SA, if to 7/2<|t| ≤ to + ¹/2 0. otherwise Carefully plot the signal, y(t), paying attention to the region when y(t) is non-zero, and labelling all axes. Calculate the Fourier transform of the signal, y(t), denoted by Y (w). Clearly show all your steps and working, but note that marks are awarded for concise approaches rather than a verbose long-winded solution. Provide an alternative derivation to calculate Y (w), different to your method in part a)(ii), and using further properties of the Fourier transform not already used. = Simplify your answer for the case to check if this solution is correct. T/2, and explain how you can
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