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6) Show that TF [f (t- a)] = e -j2nva TF [f (t)] where aeR *. %3!

6) Show that TF [f (t- a)] = e -j2nva TF [f (t)] where aeR *. %3!

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 with part 6
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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By using Fourier transform  Definition 

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