5) The function (g) is defined by: g (t) = t.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 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
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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).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F993e67b1-cdf4-4f45-8d93-da1ff9fd7b67%2F52af2645-63ff-46f1-99b2-f1ac88d46500%2Fd08cyee_processed.jpeg&w=3840&q=75)
Signal : A signal is the essential quantity for expressing some data in electrical engineering. It makes no difference if the data is analogue or digital.
There are two types of signals, which are :
Analog signals : A signal might be an analogue value, meaning it is specified in terms of time. It's a never-ending signal. Such signals are established over a number of independent variables that are continuous. They are hard to examine due to the large amount of data they include. Due to a huge data sample, they are extremely accurate. we will need to have an endless memory to store these signals since they can attain unlimited values on a real line.
Example: A person's voice.
Digital signal : Digital signals are extremely easy to analyse when compared to analogue signals. They're signals that came and go.
The term "digital" refers to discrete values, which indicates that they utilise particular values to describe data. Just two values, 1 and 0, are used to represent something as digital signal (binary values). As digital signals are discrete samples of an analogue signal obtained over a period of time, they are less accurate than analogue signals. Digital signals are not affected by noise. As a result, they last for a long time and are simple and easy to understand.
Example : Computers Keyboard.
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