Calculate the Fourier transform [on hold]

Clash Royale CLAN TAG#URR8PPP

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I need help to calculate the Fourier transform of this function:

$f(t)=sin (e^-at)$

Where $a$ is a constant.

I tried to use the definition of the Fourier transform:

$f(omega)=int_-infty^infty f(t) * e^-iomega tdt$

Substituting $f(t)$:

$f(omega)=int_-infty^infty sin (e^-at) * e^-iomega tdt$

I used the Euler's identity: $2isin theta = e^i theta-e^-i theta $

Substituting: $sin (e^-at)$ and $theta=e^-at$

$f(omega)=frac12iint_-infty^infty (e^i e^-at -e^-i e^-at) * e^-iomega tdt$

And I can't solve that integral. I don't know if the way i'm taking is the correct but i would like some help to solve it. Thanks.

fourier-transform

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edited 3 hours ago

asked 6 hours ago

Sergio Carballo Téllez

41

put on hold as off-topic by uniquesolution, Arnaud Mortier, Holo, user 108128, José Carlos Santos 5 hours ago

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – uniquesolution, Arnaud Mortier, Holo, user 108128, José Carlos Santos

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  Fourier transforms are $10 per function.
  – uniquesolution
  6 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I do them for €9 and the tenth is for free. Seriously, you will find that questions are better received if you include your background and your thoughts on the problem, up to where you are stuck and why. And also when all the relevant data are included: what is $a$?
  – Arnaud Mortier
  6 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for your comments. I am new and I did not know how to write my question properly. I'll correct it.
  – Sergio Carballo Téllez
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  If the questions is put on hold before you edit, don't worry. Edit it appropriately and it will get re-opened.
  – saulspatz
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I edited it. I hope it's OK.
  – Sergio Carballo Téllez
  3 hours ago
  
  

  
  
  
  

add a comment | 

up vote
-4
down vote

favorite

I need help to calculate the Fourier transform of this function:

$f(t)=sin (e^-at)$

Where $a$ is a constant.

I tried to use the definition of the Fourier transform:

$f(omega)=int_-infty^infty f(t) * e^-iomega tdt$

Substituting $f(t)$:

$f(omega)=int_-infty^infty sin (e^-at) * e^-iomega tdt$

I used the Euler's identity: $2isin theta = e^i theta-e^-i theta $

Substituting: $sin (e^-at)$ and $theta=e^-at$

$f(omega)=frac12iint_-infty^infty (e^i e^-at -e^-i e^-at) * e^-iomega tdt$

And I can't solve that integral. I don't know if the way i'm taking is the correct but i would like some help to solve it. Thanks.

fourier-transform

share|cite|improve this question

edited 3 hours ago

asked 6 hours ago

Sergio Carballo Téllez

41

put on hold as off-topic by uniquesolution, Arnaud Mortier, Holo, user 108128, José Carlos Santos 5 hours ago

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – uniquesolution, Arnaud Mortier, Holo, user 108128, José Carlos Santos

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  Fourier transforms are $10 per function.
  – uniquesolution
  6 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I do them for €9 and the tenth is for free. Seriously, you will find that questions are better received if you include your background and your thoughts on the problem, up to where you are stuck and why. And also when all the relevant data are included: what is $a$?
  – Arnaud Mortier
  6 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for your comments. I am new and I did not know how to write my question properly. I'll correct it.
  – Sergio Carballo Téllez
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  If the questions is put on hold before you edit, don't worry. Edit it appropriately and it will get re-opened.
  – saulspatz
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I edited it. I hope it's OK.
  – Sergio Carballo Téllez
  3 hours ago
  
  

  
  
  
  

add a comment | 

up vote
-4
down vote

favorite

up vote
-4
down vote

favorite

I need help to calculate the Fourier transform of this function:

$f(t)=sin (e^-at)$

Where $a$ is a constant.

I tried to use the definition of the Fourier transform:

$f(omega)=int_-infty^infty f(t) * e^-iomega tdt$

Substituting $f(t)$:

$f(omega)=int_-infty^infty sin (e^-at) * e^-iomega tdt$

I used the Euler's identity: $2isin theta = e^i theta-e^-i theta $

Substituting: $sin (e^-at)$ and $theta=e^-at$

$f(omega)=frac12iint_-infty^infty (e^i e^-at -e^-i e^-at) * e^-iomega tdt$

And I can't solve that integral. I don't know if the way i'm taking is the correct but i would like some help to solve it. Thanks.

fourier-transform

share|cite|improve this question

edited 3 hours ago

asked 6 hours ago

Sergio Carballo Téllez

41

I need help to calculate the Fourier transform of this function:

$f(t)=sin (e^-at)$

Where $a$ is a constant.

I tried to use the definition of the Fourier transform:

$f(omega)=int_-infty^infty f(t) * e^-iomega tdt$

Substituting $f(t)$:

$f(omega)=int_-infty^infty sin (e^-at) * e^-iomega tdt$

I used the Euler's identity: $2isin theta = e^i theta-e^-i theta $

Substituting: $sin (e^-at)$ and $theta=e^-at$

$f(omega)=frac12iint_-infty^infty (e^i e^-at -e^-i e^-at) * e^-iomega tdt$

And I can't solve that integral. I don't know if the way i'm taking is the correct but i would like some help to solve it. Thanks.

fourier-transform

share|cite|improve this question

edited 3 hours ago

asked 6 hours ago

Sergio Carballo Téllez

41

share|cite|improve this question

share|cite|improve this question

edited 3 hours ago

edited 3 hours ago

edited 3 hours ago

asked 6 hours ago

Sergio Carballo Téllez

41

asked 6 hours ago

Sergio Carballo Téllez

41

asked 6 hours ago

Sergio Carballo Téllez

41

41

put on hold as off-topic by uniquesolution, Arnaud Mortier, Holo, user 108128, José Carlos Santos 5 hours ago

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – uniquesolution, Arnaud Mortier, Holo, user 108128, José Carlos Santos

If this question can be reworded to fit the rules in the help center, please edit the question.

put on hold as off-topic by uniquesolution, Arnaud Mortier, Holo, user 108128, José Carlos Santos 5 hours ago

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question is missing context or other details: Please improve the question by providing additional context, which ideally includes your thoughts on the problem and any attempts you have made to solve it. This information helps others identify where you have difficulties and helps them write answers appropriate to your experience level." – uniquesolution, Arnaud Mortier, Holo, user 108128, José Carlos Santos

If this question can be reworded to fit the rules in the help center, please edit the question.

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  Fourier transforms are $10 per function.
  – uniquesolution
  6 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I do them for €9 and the tenth is for free. Seriously, you will find that questions are better received if you include your background and your thoughts on the problem, up to where you are stuck and why. And also when all the relevant data are included: what is $a$?
  – Arnaud Mortier
  6 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for your comments. I am new and I did not know how to write my question properly. I'll correct it.
  – Sergio Carballo Téllez
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  If the questions is put on hold before you edit, don't worry. Edit it appropriately and it will get re-opened.
  – saulspatz
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I edited it. I hope it's OK.
  – Sergio Carballo Téllez
  3 hours ago
  
  

  
  
  
  

add a comment | 

• 
  
  
  

  
  3
  

  
  
  
  
  
  

  
  Fourier transforms are $10 per function.
  – uniquesolution
  6 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I do them for €9 and the tenth is for free. Seriously, you will find that questions are better received if you include your background and your thoughts on the problem, up to where you are stuck and why. And also when all the relevant data are included: what is $a$?
  – Arnaud Mortier
  6 hours ago
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  Thanks for your comments. I am new and I did not know how to write my question properly. I'll correct it.
  – Sergio Carballo Téllez
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  If the questions is put on hold before you edit, don't worry. Edit it appropriately and it will get re-opened.
  – saulspatz
  5 hours ago
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  I edited it. I hope it's OK.
  – Sergio Carballo Téllez
  3 hours ago
  
  

  
  
  
  

3

3

Fourier transforms are $10 per function.
– uniquesolution
6 hours ago

Fourier transforms are $10 per function.
– uniquesolution
6 hours ago

I do them for €9 and the tenth is for free. Seriously, you will find that questions are better received if you include your background and your thoughts on the problem, up to where you are stuck and why. And also when all the relevant data are included: what is $a$?
– Arnaud Mortier
6 hours ago

I do them for €9 and the tenth is for free. Seriously, you will find that questions are better received if you include your background and your thoughts on the problem, up to where you are stuck and why. And also when all the relevant data are included: what is $a$?
– Arnaud Mortier
6 hours ago

Thanks for your comments. I am new and I did not know how to write my question properly. I'll correct it.
– Sergio Carballo Téllez
5 hours ago

Thanks for your comments. I am new and I did not know how to write my question properly. I'll correct it.
– Sergio Carballo Téllez
5 hours ago

If the questions is put on hold before you edit, don't worry. Edit it appropriately and it will get re-opened.
– saulspatz
5 hours ago

If the questions is put on hold before you edit, don't worry. Edit it appropriately and it will get re-opened.
– saulspatz
5 hours ago

I edited it. I hope it's OK.
– Sergio Carballo Téllez
3 hours ago

I edited it. I hope it's OK.
– Sergio Carballo Téllez
3 hours ago

add a comment | 

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