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4) Show that, TF[f(t)] = -2 fo f(t) sin(2nvt)dt, in the case where the function (f) is odd. 5) The function (g) is defined by: g(t) = t2.n(t), Where (t), indicates the function 'door' (i) Define the 'door' function. (ii) Give the graphical representation of the function (g). (iii) Determine TF [g (t)). 6) Show that, TF[fS(t- a)] = e-12mva TF[f(t)], where a E R*

4) Show that, TF[f(t)] = -2 fo f(t) sin(2nvt)dt, in the case where the function (f) is odd. 5) The function (g) is defined by: g(t) = t2.n(t), Where (t), indicates the function 'door' (i) Define the 'door' function. (ii) Give the graphical representation of the function (g). (iii) Determine TF [g (t)). 6) Show that, TF[fS(t- a)] = e-12mva TF[f(t)], where a E R*

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 please answer part part 4 to 7 

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Question 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. 2) Give a physical interpretation of the Fourier transform of a function. TF [f (t)] denotes the Fourier transform of a function (f). 3) Show that, TF[f(t)] = 2 f(t) cos(2nvt)dt, in the case where the function (f) is %3D even. too 4) Show that, TF[f(t)] = -2 f(t) sin(2nvt)dt, in the case where the function (f) is odd. 5) The function (g) is defined by: g(t) = t2.n(t), Where n(t), indicates the function 'door' (i) Define the 'door' function. (ii) Give the graphical representation of the function (g). (iii) Determine TE [g (t)]. 6) Show that, TF[f(t – a)] = e-j2rva TF[f(t)], where a E R* %3D 7) The function (h) is defined by: h(t) = 0 if te]-o, 0[; h(t) = t2 – t+ 0,25 if te [0, 1[;h(t) = 0 ifte [1, +o[. (i) Give the graphical representation of the function (h). (ii) Using the previous results, determine the Fourier transform of the function (h).
Transcribed Image Text:Question 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. 2) Give a physical interpretation of the Fourier transform of a function. TF [f (t)] denotes the Fourier transform of a function (f). 3) Show that, TF[f(t)] = 2 f(t) cos(2nvt)dt, in the case where the function (f) is %3D even. too 4) Show that, TF[f(t)] = -2 f(t) sin(2nvt)dt, in the case where the function (f) is odd. 5) The function (g) is defined by: g(t) = t2.n(t), Where n(t), indicates the function 'door' (i) Define the 'door' function. (ii) Give the graphical representation of the function (g). (iii) Determine TE [g (t)]. 6) Show that, TF[f(t – a)] = e-j2rva TF[f(t)], where a E R* %3D 7) The function (h) is defined by: h(t) = 0 if te]-o, 0[; h(t) = t2 – t+ 0,25 if te [0, 1[;h(t) = 0 ifte [1, +o[. (i) Give the graphical representation of the function (h). (ii) Using the previous results, determine the Fourier transform of the function (h).
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