Exercise 1: (iii) Determine TF [g (t)]. 6) Show that TF [f (t - a)] = e-2nva TE (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, + o [. TF [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 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'.

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...
icon
Related questions
Question
Please help with part 7
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).
Expert Solution
steps

Step by step

Solved in 3 steps with 1 images

Blurred answer
Similar questions
  • SEE MORE QUESTIONS
Recommended textbooks for you
Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
Electrical Engineering
ISBN:
9780133923605
Author:
Robert L. Boylestad
Publisher:
PEARSON
Delmar's Standard Textbook Of Electricity
Delmar's Standard Textbook Of Electricity
Electrical Engineering
ISBN:
9781337900348
Author:
Stephen L. Herman
Publisher:
Cengage Learning
Programmable Logic Controllers
Programmable Logic Controllers
Electrical Engineering
ISBN:
9780073373843
Author:
Frank D. Petruzella
Publisher:
McGraw-Hill Education
Fundamentals of Electric Circuits
Fundamentals of Electric Circuits
Electrical Engineering
ISBN:
9780078028229
Author:
Charles K Alexander, Matthew Sadiku
Publisher:
McGraw-Hill Education
Electric Circuits. (11th Edition)
Electric Circuits. (11th Edition)
Electrical Engineering
ISBN:
9780134746968
Author:
James W. Nilsson, Susan Riedel
Publisher:
PEARSON
Engineering Electromagnetics
Engineering Electromagnetics
Electrical Engineering
ISBN:
9780078028151
Author:
Hayt, William H. (william Hart), Jr, BUCK, John A.
Publisher:
Mcgraw-hill Education,