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

Introductory Circuit Analysis (13th Edition)
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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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