Fourier Transform Help Needed Announcing the arrival of Valued Associate #679: Cesar Manara Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Fourier transform integralFourier transform in $mathbb R^3$Hilbert transform and Fourier transformMisunderstanding with Fourier sine transform…Help with Fourier transformNeed help with a Fourier Transform QuestionFourier transform of $te^-t^2$?What is difference between Fourier Transform and Fast Fourier Transform?Fourier Transform of SineHelp needed in solving this problem of Fourier Transform

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Fourier Transform Help Needed



Announcing the arrival of Valued Associate #679: Cesar Manara
Planned maintenance scheduled April 17/18, 2019 at 00:00UTC (8:00pm US/Eastern)Fourier transform integralFourier transform in $mathbb R^3$Hilbert transform and Fourier transformMisunderstanding with Fourier sine transform…Help with Fourier transformNeed help with a Fourier Transform QuestionFourier transform of $te^-t^2$?What is difference between Fourier Transform and Fast Fourier Transform?Fourier Transform of SineHelp needed in solving this problem of Fourier Transform










1












$begingroup$


I need help with a Fourier Transform problem for a composite waveform for an assignment. I'm stumped with how to approach this one.



Waveform



The only way I could think of to solve this was by considering it as a six-part piecewise function, but this seemed very long and complicated. Another user on this site asked me to write my function as sum of a triangle and two rectangles.



I tried adding the following waveforms
Triangular - -3 to +3 with height 3
Rectangular - -2 to 2 with height 1
Rectangular - -1 to 1 with height 1



I plotted them in MATLAB and ended up with this:



Simulation



The vertical lines that connect the segments are a problem. Is there any way to just translate the required segments upwards without the lines? Also am I doing this wrong? Any help with solving this one would be really appreciated :)






functions fourier-analysis integral-transforms







share|cite|improve this question











$endgroup$







  • 1




    $begingroup$
    The lines are completely irrelevant. It's the very same function. MATLAB draws the lines because it generates the plot by simply evaluating the function on some number of points, and then "connects the dots". If, OTOH, you draw the plot yourself, you know that it has infinite slopy at $-2,-1,1,2$ and omit the line there...
    $endgroup$
    – fgp
    Mar 2 '14 at 13:59










  • $begingroup$
    Oh, and the hand-drawn plot isn't strictly speaking well-defined either. It doesn't include the vertical lines, but it also fails to tell you what the function's value at the discontinuous points $-2,-1,1,2$ actually is. For $-2$ it could be $1$ or $2$. Which one it is is often indicated by placing a filled dot at the point corresponding to the value the function takes, and just a circle at the other end of the discontinuity.
    $endgroup$
    – fgp
    Mar 2 '14 at 14:01






  • 1




    $begingroup$
    Yes, so far that is right, $$f(x)=max(0,3-|x|)+rect(x/2)+rect(x).$$ Now the Fourier transforms are all linear, so that you can compute it for each term separately and then sum it up.
    $endgroup$
    – LutzL
    Mar 2 '14 at 14:05










  • $begingroup$
    Thanks so much :). So when finding the Transform can I use the lines y= 1 between -1 and +1 and y =1 between -2 and +2 for the rectangles? Something like this s18.postimg.org/iyoxji3c9/working.jpg
    $endgroup$
    – user2802349
    Mar 2 '14 at 15:10










  • $begingroup$
    Could someone tell me if that ^ method is right? :(
    $endgroup$
    – user2802349
    Mar 3 '14 at 16:03















1












$begingroup$


I need help with a Fourier Transform problem for a composite waveform for an assignment. I'm stumped with how to approach this one.



Waveform



The only way I could think of to solve this was by considering it as a six-part piecewise function, but this seemed very long and complicated. Another user on this site asked me to write my function as sum of a triangle and two rectangles.



I tried adding the following waveforms
Triangular - -3 to +3 with height 3
Rectangular - -2 to 2 with height 1
Rectangular - -1 to 1 with height 1



I plotted them in MATLAB and ended up with this:



Simulation



The vertical lines that connect the segments are a problem. Is there any way to just translate the required segments upwards without the lines? Also am I doing this wrong? Any help with solving this one would be really appreciated :)






functions fourier-analysis integral-transforms







share|cite|improve this question











$endgroup$







  • 1




    $begingroup$
    The lines are completely irrelevant. It's the very same function. MATLAB draws the lines because it generates the plot by simply evaluating the function on some number of points, and then "connects the dots". If, OTOH, you draw the plot yourself, you know that it has infinite slopy at $-2,-1,1,2$ and omit the line there...
    $endgroup$
    – fgp
    Mar 2 '14 at 13:59










  • $begingroup$
    Oh, and the hand-drawn plot isn't strictly speaking well-defined either. It doesn't include the vertical lines, but it also fails to tell you what the function's value at the discontinuous points $-2,-1,1,2$ actually is. For $-2$ it could be $1$ or $2$. Which one it is is often indicated by placing a filled dot at the point corresponding to the value the function takes, and just a circle at the other end of the discontinuity.
    $endgroup$
    – fgp
    Mar 2 '14 at 14:01






  • 1




    $begingroup$
    Yes, so far that is right, $$f(x)=max(0,3-|x|)+rect(x/2)+rect(x).$$ Now the Fourier transforms are all linear, so that you can compute it for each term separately and then sum it up.
    $endgroup$
    – LutzL
    Mar 2 '14 at 14:05










  • $begingroup$
    Thanks so much :). So when finding the Transform can I use the lines y= 1 between -1 and +1 and y =1 between -2 and +2 for the rectangles? Something like this s18.postimg.org/iyoxji3c9/working.jpg
    $endgroup$
    – user2802349
    Mar 2 '14 at 15:10










  • $begingroup$
    Could someone tell me if that ^ method is right? :(
    $endgroup$
    – user2802349
    Mar 3 '14 at 16:03













1












1








1





$begingroup$


I need help with a Fourier Transform problem for a composite waveform for an assignment. I'm stumped with how to approach this one.



Waveform



The only way I could think of to solve this was by considering it as a six-part piecewise function, but this seemed very long and complicated. Another user on this site asked me to write my function as sum of a triangle and two rectangles.



I tried adding the following waveforms
Triangular - -3 to +3 with height 3
Rectangular - -2 to 2 with height 1
Rectangular - -1 to 1 with height 1



I plotted them in MATLAB and ended up with this:



Simulation



The vertical lines that connect the segments are a problem. Is there any way to just translate the required segments upwards without the lines? Also am I doing this wrong? Any help with solving this one would be really appreciated :)






functions fourier-analysis integral-transforms







share|cite|improve this question











$endgroup$




I need help with a Fourier Transform problem for a composite waveform for an assignment. I'm stumped with how to approach this one.



Waveform



The only way I could think of to solve this was by considering it as a six-part piecewise function, but this seemed very long and complicated. Another user on this site asked me to write my function as sum of a triangle and two rectangles.



I tried adding the following waveforms
Triangular - -3 to +3 with height 3
Rectangular - -2 to 2 with height 1
Rectangular - -1 to 1 with height 1



I plotted them in MATLAB and ended up with this:



Simulation



The vertical lines that connect the segments are a problem. Is there any way to just translate the required segments upwards without the lines? Also am I doing this wrong? Any help with solving this one would be really appreciated :)






functions fourier-analysis integral-transforms




functions fourier-analysis integral-transforms






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








edited Mar 26 at 8:32









Glorfindel

3,41381930




3,41381930










asked Mar 2 '14 at 13:48









user2802349user2802349

2416




2416







  • 1




    $begingroup$
    The lines are completely irrelevant. It's the very same function. MATLAB draws the lines because it generates the plot by simply evaluating the function on some number of points, and then "connects the dots". If, OTOH, you draw the plot yourself, you know that it has infinite slopy at $-2,-1,1,2$ and omit the line there...
    $endgroup$
    – fgp
    Mar 2 '14 at 13:59










  • $begingroup$
    Oh, and the hand-drawn plot isn't strictly speaking well-defined either. It doesn't include the vertical lines, but it also fails to tell you what the function's value at the discontinuous points $-2,-1,1,2$ actually is. For $-2$ it could be $1$ or $2$. Which one it is is often indicated by placing a filled dot at the point corresponding to the value the function takes, and just a circle at the other end of the discontinuity.
    $endgroup$
    – fgp
    Mar 2 '14 at 14:01






  • 1




    $begingroup$
    Yes, so far that is right, $$f(x)=max(0,3-|x|)+rect(x/2)+rect(x).$$ Now the Fourier transforms are all linear, so that you can compute it for each term separately and then sum it up.
    $endgroup$
    – LutzL
    Mar 2 '14 at 14:05










  • $begingroup$
    Thanks so much :). So when finding the Transform can I use the lines y= 1 between -1 and +1 and y =1 between -2 and +2 for the rectangles? Something like this s18.postimg.org/iyoxji3c9/working.jpg
    $endgroup$
    – user2802349
    Mar 2 '14 at 15:10










  • $begingroup$
    Could someone tell me if that ^ method is right? :(
    $endgroup$
    – user2802349
    Mar 3 '14 at 16:03












  • 1




    $begingroup$
    The lines are completely irrelevant. It's the very same function. MATLAB draws the lines because it generates the plot by simply evaluating the function on some number of points, and then "connects the dots". If, OTOH, you draw the plot yourself, you know that it has infinite slopy at $-2,-1,1,2$ and omit the line there...
    $endgroup$
    – fgp
    Mar 2 '14 at 13:59










  • $begingroup$
    Oh, and the hand-drawn plot isn't strictly speaking well-defined either. It doesn't include the vertical lines, but it also fails to tell you what the function's value at the discontinuous points $-2,-1,1,2$ actually is. For $-2$ it could be $1$ or $2$. Which one it is is often indicated by placing a filled dot at the point corresponding to the value the function takes, and just a circle at the other end of the discontinuity.
    $endgroup$
    – fgp
    Mar 2 '14 at 14:01






  • 1




    $begingroup$
    Yes, so far that is right, $$f(x)=max(0,3-|x|)+rect(x/2)+rect(x).$$ Now the Fourier transforms are all linear, so that you can compute it for each term separately and then sum it up.
    $endgroup$
    – LutzL
    Mar 2 '14 at 14:05










  • $begingroup$
    Thanks so much :). So when finding the Transform can I use the lines y= 1 between -1 and +1 and y =1 between -2 and +2 for the rectangles? Something like this s18.postimg.org/iyoxji3c9/working.jpg
    $endgroup$
    – user2802349
    Mar 2 '14 at 15:10










  • $begingroup$
    Could someone tell me if that ^ method is right? :(
    $endgroup$
    – user2802349
    Mar 3 '14 at 16:03







1




1




$begingroup$
The lines are completely irrelevant. It's the very same function. MATLAB draws the lines because it generates the plot by simply evaluating the function on some number of points, and then "connects the dots". If, OTOH, you draw the plot yourself, you know that it has infinite slopy at $-2,-1,1,2$ and omit the line there...
$endgroup$
– fgp
Mar 2 '14 at 13:59




$begingroup$
The lines are completely irrelevant. It's the very same function. MATLAB draws the lines because it generates the plot by simply evaluating the function on some number of points, and then "connects the dots". If, OTOH, you draw the plot yourself, you know that it has infinite slopy at $-2,-1,1,2$ and omit the line there...
$endgroup$
– fgp
Mar 2 '14 at 13:59












$begingroup$
Oh, and the hand-drawn plot isn't strictly speaking well-defined either. It doesn't include the vertical lines, but it also fails to tell you what the function's value at the discontinuous points $-2,-1,1,2$ actually is. For $-2$ it could be $1$ or $2$. Which one it is is often indicated by placing a filled dot at the point corresponding to the value the function takes, and just a circle at the other end of the discontinuity.
$endgroup$
– fgp
Mar 2 '14 at 14:01




$begingroup$
Oh, and the hand-drawn plot isn't strictly speaking well-defined either. It doesn't include the vertical lines, but it also fails to tell you what the function's value at the discontinuous points $-2,-1,1,2$ actually is. For $-2$ it could be $1$ or $2$. Which one it is is often indicated by placing a filled dot at the point corresponding to the value the function takes, and just a circle at the other end of the discontinuity.
$endgroup$
– fgp
Mar 2 '14 at 14:01




1




1




$begingroup$
Yes, so far that is right, $$f(x)=max(0,3-|x|)+rect(x/2)+rect(x).$$ Now the Fourier transforms are all linear, so that you can compute it for each term separately and then sum it up.
$endgroup$
– LutzL
Mar 2 '14 at 14:05




$begingroup$
Yes, so far that is right, $$f(x)=max(0,3-|x|)+rect(x/2)+rect(x).$$ Now the Fourier transforms are all linear, so that you can compute it for each term separately and then sum it up.
$endgroup$
– LutzL
Mar 2 '14 at 14:05












$begingroup$
Thanks so much :). So when finding the Transform can I use the lines y= 1 between -1 and +1 and y =1 between -2 and +2 for the rectangles? Something like this s18.postimg.org/iyoxji3c9/working.jpg
$endgroup$
– user2802349
Mar 2 '14 at 15:10




$begingroup$
Thanks so much :). So when finding the Transform can I use the lines y= 1 between -1 and +1 and y =1 between -2 and +2 for the rectangles? Something like this s18.postimg.org/iyoxji3c9/working.jpg
$endgroup$
– user2802349
Mar 2 '14 at 15:10












$begingroup$
Could someone tell me if that ^ method is right? :(
$endgroup$
– user2802349
Mar 3 '14 at 16:03




$begingroup$
Could someone tell me if that ^ method is right? :(
$endgroup$
– user2802349
Mar 3 '14 at 16:03










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