Inverse Fourier transform (in frequency) of a rectangular pulse
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This is my first question on here so I'm new to the formatting and all so please be indulgent :)
I have an exam question where I am given a function H(f) that is a rectangular pulse between -fc and fc (where fc is a given frequency) of amplitude 1 and I need to calculate it's inverse Fourier transform. I've looked around online and could only find vague answers and not in the frequency domain.
Alternatively, if some of you want to think a little more, I have a given signal x(t) which is also a rectangular pulse between -d and d of amplitude A, I have it's frequency Fourier transform which is
X(f) = 2*A*d*sinc(2*pi*f*d)
I then have to convert x(t) into xp(t) where xp(t) is the periodic version of x(t) of period T and Xp(f) is the fourier transform of xp(t).
Assuming I now have xp(t), Xp(f) and H(f), the full question is:
We set xp(t) at the input of h(t), determine the range of frequencies fc such that the output signal y(t) is a sine function. To solve this I must either calculate a convolution of xp(t) and h(t) to get y(t) as a sine function or multiply Xp(f) and H(f), find Y(f) such that its inverse Fourier transform is a sine function.
I know that the fourier transform of a sine function is:
(1/2j)*[dirac(f-f0)-dirac(f+f0)]
fourier-transform convolution
edited Dec 15 '18 at 22:05
Bernard
122k740116
asked Dec 15 '18 at 22:03
Max MichelMax Michel
32
$endgroup$
|
show 6 more comments
$begingroup$
This is my first question on here so I'm new to the formatting and all so please be indulgent :)
I have an exam question where I am given a function H(f) that is a rectangular pulse between -fc and fc (where fc is a given frequency) of amplitude 1 and I need to calculate it's inverse Fourier transform. I've looked around online and could only find vague answers and not in the frequency domain.
Alternatively, if some of you want to think a little more, I have a given signal x(t) which is also a rectangular pulse between -d and d of amplitude A, I have it's frequency Fourier transform which is
X(f) = 2*A*d*sinc(2*pi*f*d)
I then have to convert x(t) into xp(t) where xp(t) is the periodic version of x(t) of period T and Xp(f) is the fourier transform of xp(t).
Assuming I now have xp(t), Xp(f) and H(f), the full question is:
We set xp(t) at the input of h(t), determine the range of frequencies fc such that the output signal y(t) is a sine function. To solve this I must either calculate a convolution of xp(t) and h(t) to get y(t) as a sine function or multiply Xp(f) and H(f), find Y(f) such that its inverse Fourier transform is a sine function.
I know that the fourier transform of a sine function is:
(1/2j)*[dirac(f-f0)-dirac(f+f0)]
fourier-transform convolution
edited Dec 15 '18 at 22:05
Bernard
122k740116
asked Dec 15 '18 at 22:03
Max MichelMax Michel
32
$endgroup$
$begingroup$
Thank you for the edit! I didn't notice all the mistakes...
$endgroup$
– Max Michel
Dec 15 '18 at 22:06
$begingroup$
You are not allowed to post three questions in a single answer. Obviously, your homework-like question has three parts and you are trying to have it solved for you here, which is not a good idea.
$endgroup$
– msm
Dec 15 '18 at 22:07
$begingroup$
I see @msm, I should explain that this isn't homework but revision for an upcoming exam which is why there are many parts. I would love to be able to make the question more acceptable, I'm just not sure which parts are crucial to finding the right path to the answer...
$endgroup$
– Max Michel
Dec 15 '18 at 22:10
$begingroup$
Look at Rules 201, 202 in en.wikipedia.org/wiki/…. I'm not sure what is vague there.
$endgroup$
– copper.hat
Dec 15 '18 at 22:16
$begingroup$
What do you mean by set xp(t) at the input of h(t)? Where did h(t) come from?
$endgroup$
– copper.hat
Dec 15 '18 at 22:17
|
show 6 more comments
$begingroup$
This is my first question on here so I'm new to the formatting and all so please be indulgent :)
I have an exam question where I am given a function H(f) that is a rectangular pulse between -fc and fc (where fc is a given frequency) of amplitude 1 and I need to calculate it's inverse Fourier transform. I've looked around online and could only find vague answers and not in the frequency domain.
Alternatively, if some of you want to think a little more, I have a given signal x(t) which is also a rectangular pulse between -d and d of amplitude A, I have it's frequency Fourier transform which is
X(f) = 2*A*d*sinc(2*pi*f*d)
I then have to convert x(t) into xp(t) where xp(t) is the periodic version of x(t) of period T and Xp(f) is the fourier transform of xp(t).
Assuming I now have xp(t), Xp(f) and H(f), the full question is:
We set xp(t) at the input of h(t), determine the range of frequencies fc such that the output signal y(t) is a sine function. To solve this I must either calculate a convolution of xp(t) and h(t) to get y(t) as a sine function or multiply Xp(f) and H(f), find Y(f) such that its inverse Fourier transform is a sine function.
I know that the fourier transform of a sine function is:
(1/2j)*[dirac(f-f0)-dirac(f+f0)]
fourier-transform convolution
edited Dec 15 '18 at 22:05
Bernard
122k740116
asked Dec 15 '18 at 22:03
Max MichelMax Michel
32
$endgroup$
This is my first question on here so I'm new to the formatting and all so please be indulgent :)
I have an exam question where I am given a function H(f) that is a rectangular pulse between -fc and fc (where fc is a given frequency) of amplitude 1 and I need to calculate it's inverse Fourier transform. I've looked around online and could only find vague answers and not in the frequency domain.
Alternatively, if some of you want to think a little more, I have a given signal x(t) which is also a rectangular pulse between -d and d of amplitude A, I have it's frequency Fourier transform which is
X(f) = 2*A*d*sinc(2*pi*f*d)
I then have to convert x(t) into xp(t) where xp(t) is the periodic version of x(t) of period T and Xp(f) is the fourier transform of xp(t).
Assuming I now have xp(t), Xp(f) and H(f), the full question is:
We set xp(t) at the input of h(t), determine the range of frequencies fc such that the output signal y(t) is a sine function. To solve this I must either calculate a convolution of xp(t) and h(t) to get y(t) as a sine function or multiply Xp(f) and H(f), find Y(f) such that its inverse Fourier transform is a sine function.
I know that the fourier transform of a sine function is:
(1/2j)*[dirac(f-f0)-dirac(f+f0)]
fourier-transform convolution
fourier-transform convolution
edited Dec 15 '18 at 22:05
Bernard
122k740116
asked Dec 15 '18 at 22:03
Max MichelMax Michel
32
edited Dec 15 '18 at 22:05
Bernard
122k740116
asked Dec 15 '18 at 22:03
Max MichelMax Michel
32
edited Dec 15 '18 at 22:05
Bernard
122k740116
edited Dec 15 '18 at 22:05
Bernard
122k740116
edited Dec 15 '18 at 22:05
Bernard
122k740116
122k740116
asked Dec 15 '18 at 22:03
Max MichelMax Michel
32
asked Dec 15 '18 at 22:03
Max MichelMax Michel
32
asked Dec 15 '18 at 22:03
Max MichelMax Michel
32
32
$begingroup$
Thank you for the edit! I didn't notice all the mistakes...
$endgroup$
– Max Michel
Dec 15 '18 at 22:06
$begingroup$
You are not allowed to post three questions in a single answer. Obviously, your homework-like question has three parts and you are trying to have it solved for you here, which is not a good idea.
$endgroup$
– msm
Dec 15 '18 at 22:07
$begingroup$
I see @msm, I should explain that this isn't homework but revision for an upcoming exam which is why there are many parts. I would love to be able to make the question more acceptable, I'm just not sure which parts are crucial to finding the right path to the answer...
$endgroup$
– Max Michel
Dec 15 '18 at 22:10
$begingroup$
Look at Rules 201, 202 in en.wikipedia.org/wiki/…. I'm not sure what is vague there.
$endgroup$
– copper.hat
Dec 15 '18 at 22:16
$begingroup$
What do you mean by set xp(t) at the input of h(t)? Where did h(t) come from?
$endgroup$
– copper.hat
Dec 15 '18 at 22:17
|
show 6 more comments
$begingroup$
Thank you for the edit! I didn't notice all the mistakes...
$endgroup$
– Max Michel
Dec 15 '18 at 22:06
$begingroup$
You are not allowed to post three questions in a single answer. Obviously, your homework-like question has three parts and you are trying to have it solved for you here, which is not a good idea.
$endgroup$
– msm
Dec 15 '18 at 22:07
$begingroup$
I see @msm, I should explain that this isn't homework but revision for an upcoming exam which is why there are many parts. I would love to be able to make the question more acceptable, I'm just not sure which parts are crucial to finding the right path to the answer...
$endgroup$
– Max Michel
Dec 15 '18 at 22:10
$begingroup$
Look at Rules 201, 202 in en.wikipedia.org/wiki/…. I'm not sure what is vague there.
$endgroup$
– copper.hat
Dec 15 '18 at 22:16
$begingroup$
What do you mean by set xp(t) at the input of h(t)? Where did h(t) come from?
$endgroup$
– copper.hat
Dec 15 '18 at 22:17
$begingroup$
Thank you for the edit! I didn't notice all the mistakes...
$endgroup$
– Max Michel
Dec 15 '18 at 22:06
$begingroup$
Thank you for the edit! I didn't notice all the mistakes...
$endgroup$
– Max Michel
Dec 15 '18 at 22:06
$begingroup$
You are not allowed to post three questions in a single answer. Obviously, your homework-like question has three parts and you are trying to have it solved for you here, which is not a good idea.
$endgroup$
– msm
Dec 15 '18 at 22:07
$begingroup$
You are not allowed to post three questions in a single answer. Obviously, your homework-like question has three parts and you are trying to have it solved for you here, which is not a good idea.
$endgroup$
– msm
Dec 15 '18 at 22:07
$begingroup$
I see @msm, I should explain that this isn't homework but revision for an upcoming exam which is why there are many parts. I would love to be able to make the question more acceptable, I'm just not sure which parts are crucial to finding the right path to the answer...
$endgroup$
– Max Michel
Dec 15 '18 at 22:10
$begingroup$
I see @msm, I should explain that this isn't homework but revision for an upcoming exam which is why there are many parts. I would love to be able to make the question more acceptable, I'm just not sure which parts are crucial to finding the right path to the answer...
$endgroup$
– Max Michel
Dec 15 '18 at 22:10
$begingroup$
Look at Rules 201, 202 in en.wikipedia.org/wiki/…. I'm not sure what is vague there.
$endgroup$
– copper.hat
Dec 15 '18 at 22:16
$begingroup$
Look at Rules 201, 202 in en.wikipedia.org/wiki/…. I'm not sure what is vague there.
$endgroup$
– copper.hat
Dec 15 '18 at 22:16
$begingroup$
What do you mean by set xp(t) at the input of h(t)? Where did h(t) come from?
$endgroup$
– copper.hat
Dec 15 '18 at 22:17
$begingroup$
What do you mean by set xp(t) at the input of h(t)? Where did h(t) come from?
$endgroup$
– copper.hat
Dec 15 '18 at 22:17
|
show 6 more comments
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$begingroup$
Thank you for the edit! I didn't notice all the mistakes...
$endgroup$
– Max Michel
Dec 15 '18 at 22:06
$begingroup$
You are not allowed to post three questions in a single answer. Obviously, your homework-like question has three parts and you are trying to have it solved for you here, which is not a good idea.
$endgroup$
– msm
Dec 15 '18 at 22:07
$begingroup$
I see @msm, I should explain that this isn't homework but revision for an upcoming exam which is why there are many parts. I would love to be able to make the question more acceptable, I'm just not sure which parts are crucial to finding the right path to the answer...
$endgroup$
– Max Michel
Dec 15 '18 at 22:10
$begingroup$
Look at Rules 201, 202 in en.wikipedia.org/wiki/…. I'm not sure what is vague there.
$endgroup$
– copper.hat
Dec 15 '18 at 22:16
$begingroup$
What do you mean by set xp(t) at the input of h(t)? Where did h(t) come from?
$endgroup$
– copper.hat
Dec 15 '18 at 22:17