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Exercise 1: (iii) Determine TF [g (t)]. 6) Show that TF [f (t- a)] = e -j2rva TF [f (t)] where aER *. 1) Let f be a function of the real variable t, absolutely integrable over R and continuous over a closed interval. Define the Fourier transform of this function. 7) The function (h) is defined by: h (t) = 0 if te] -0, 0 [;h (t) = t2 - t + 0.25 if te [0, 1 [; h 2) Give a physical interpretation of the Fourier transform of a function. (t) = 0 if te [1, + ∞ [. TE [f (t)] denotes the Fourier transform of a function (f). (i) Give the graphical representation of the function (h). (ii) Using the previous results, determine the Fourier transform of the function (h). 31 Show that TE [f(t)] = 2 J, f(t) cos(2nvt)dt in the case where the function (f) is End of document even. 4) Show that TE[f(t)] = -2j J. f(t) sin(2nvt) dt in the case where the function (f) is odd. 5) The function (g) is defined by: g (t) = t2.II (t), Where II (t) indicates the function 'door'. (i) Define the 'door' function. (ii) Give the graphical representation of the function (g).

Exercise 1: (iii) Determine TF [g (t)]. 6) Show that TF [f (t- a)] = e -j2rva TF [f (t)] where aER *. 1) Let f be a function of the real variable t, absolutely integrable over R and continuous over a closed interval. Define the Fourier transform of this function. 7) The function (h) is defined by: h (t) = 0 if te] -0, 0 [;h (t) = t2 - t + 0.25 if te [0, 1 [; h 2) Give a physical interpretation of the Fourier transform of a function. (t) = 0 if te [1, + ∞ [. TE [f (t)] denotes the Fourier transform of a function (f). (i) Give the graphical representation of the function (h). (ii) Using the previous results, determine the Fourier transform of the function (h). 31 Show that TE [f(t)] = 2 J, f(t) cos(2nvt)dt in the case where the function (f) is End of document even. 4) Show that TE[f(t)] = -2j J. f(t) sin(2nvt) dt in the case where the function (f) is odd. 5) The function (g) is defined by: g (t) = t2.II (t), Where II (t) indicates the function 'door'. (i) Define the 'door' function. (ii) Give the graphical representation of the function (g).

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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Can you help me only with part 7. Thanks
Exercise 1: (iii) Determine TE [g (t)]. 6) Show that TF [f (t – a)] = e -j2rva TF [f (t)] where aER *. 1) Let f be a function of the real variable t, absolutely integrable over R and continuous over a closed interval. Define the Fourier transform of this function. 7) The function (h) is defined by: h (t) = 0 if te] -∞, 0 [; h (t) = t2 - t + 0.25 if te [0, 1 [; h 2) Give a physical interpretation of the Fourier transform of a function. (t) = 0 if te [1, + ∞ [. TE [f (t)] denotes the Fourier transform of a function (f). (i) Give the graphical representation of the function (h). (ii) Using the previous results, determine the Fourier transform of the function (h). 3) Show that TF [f(t)] = 2 J, f(t) cos(2nvt)dt in the case where the function (f) is End of document even. 4) Show that TF[f(t)] = -2j J. f(t) sin(2nvt) dt in the case where the function (f) is odd. 5) The function (g) is defined by: g (t) = t2.II (t), Where II (t) indicates the function 'door'. (i) Define the 'door' function. (ii) Give the graphical representation of the function (g).
Transcribed Image Text:Exercise 1: (iii) Determine TE [g (t)]. 6) Show that TF [f (t – a)] = e -j2rva TF [f (t)] where aER *. 1) Let f be a function of the real variable t, absolutely integrable over R and continuous over a closed interval. Define the Fourier transform of this function. 7) The function (h) is defined by: h (t) = 0 if te] -∞, 0 [; h (t) = t2 - t + 0.25 if te [0, 1 [; h 2) Give a physical interpretation of the Fourier transform of a function. (t) = 0 if te [1, + ∞ [. TE [f (t)] denotes the Fourier transform of a function (f). (i) Give the graphical representation of the function (h). (ii) Using the previous results, determine the Fourier transform of the function (h). 3) Show that TF [f(t)] = 2 J, f(t) cos(2nvt)dt in the case where the function (f) is End of document even. 4) Show that TF[f(t)] = -2j J. f(t) sin(2nvt) dt in the case where the function (f) is odd. 5) The function (g) is defined by: g (t) = t2.II (t), Where II (t) indicates the function 'door'. (i) Define the 'door' function. (ii) Give the graphical representation of the function (g).
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