Fourier transformation of $e^-at$ from $0$ to $T$
Clash Royale CLAN TAG#URR8PPP
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I have to find the fourier transform of $g(t)$. Picture is added at the link below.
https://www.mathcha.io/editor/KkvMFWBUm3TXrhr0
I have tried this way
beginalign
G(f)&=int ^infty _-infty g( t) e^-jomega t, dt\
&=int ^infty _-infty e^-at rectleft(fractT -frac12right) e^-jomega t, dt\
&=int ^T_0 e^-at e^-jomega t, dt\
&=frac1-e^-( a+jomega ) Ta+jomega
endalign
where $$
rect(t) ~is ~unit ~rectangular ~function\
rect(fractT-frac12) = begingather*
begincases
1 & textfor 0le tle T\
0 & textfor elsewhere
endcases
endgather*
$$
But i am not sure whether it's right or not.
fourier-transform
add a comment |Â
up vote
0
down vote
favorite
I have to find the fourier transform of $g(t)$. Picture is added at the link below.
https://www.mathcha.io/editor/KkvMFWBUm3TXrhr0
I have tried this way
beginalign
G(f)&=int ^infty _-infty g( t) e^-jomega t, dt\
&=int ^infty _-infty e^-at rectleft(fractT -frac12right) e^-jomega t, dt\
&=int ^T_0 e^-at e^-jomega t, dt\
&=frac1-e^-( a+jomega ) Ta+jomega
endalign
where $$
rect(t) ~is ~unit ~rectangular ~function\
rect(fractT-frac12) = begingather*
begincases
1 & textfor 0le tle T\
0 & textfor elsewhere
endcases
endgather*
$$
But i am not sure whether it's right or not.
fourier-transform
What is "rect"?
â Lord Shark the Unknown
Sep 2 at 6:41
Then I'd say that both "rect" and the second line of your calculation are unnecessary.
â Lord Shark the Unknown
Sep 2 at 6:55
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
I have to find the fourier transform of $g(t)$. Picture is added at the link below.
https://www.mathcha.io/editor/KkvMFWBUm3TXrhr0
I have tried this way
beginalign
G(f)&=int ^infty _-infty g( t) e^-jomega t, dt\
&=int ^infty _-infty e^-at rectleft(fractT -frac12right) e^-jomega t, dt\
&=int ^T_0 e^-at e^-jomega t, dt\
&=frac1-e^-( a+jomega ) Ta+jomega
endalign
where $$
rect(t) ~is ~unit ~rectangular ~function\
rect(fractT-frac12) = begingather*
begincases
1 & textfor 0le tle T\
0 & textfor elsewhere
endcases
endgather*
$$
But i am not sure whether it's right or not.
fourier-transform
I have to find the fourier transform of $g(t)$. Picture is added at the link below.
https://www.mathcha.io/editor/KkvMFWBUm3TXrhr0
I have tried this way
beginalign
G(f)&=int ^infty _-infty g( t) e^-jomega t, dt\
&=int ^infty _-infty e^-at rectleft(fractT -frac12right) e^-jomega t, dt\
&=int ^T_0 e^-at e^-jomega t, dt\
&=frac1-e^-( a+jomega ) Ta+jomega
endalign
where $$
rect(t) ~is ~unit ~rectangular ~function\
rect(fractT-frac12) = begingather*
begincases
1 & textfor 0le tle T\
0 & textfor elsewhere
endcases
endgather*
$$
But i am not sure whether it's right or not.
fourier-transform
fourier-transform
edited Sep 2 at 7:12
asked Sep 2 at 6:34
Leolime
11
11
What is "rect"?
â Lord Shark the Unknown
Sep 2 at 6:41
Then I'd say that both "rect" and the second line of your calculation are unnecessary.
â Lord Shark the Unknown
Sep 2 at 6:55
add a comment |Â
What is "rect"?
â Lord Shark the Unknown
Sep 2 at 6:41
Then I'd say that both "rect" and the second line of your calculation are unnecessary.
â Lord Shark the Unknown
Sep 2 at 6:55
What is "rect"?
â Lord Shark the Unknown
Sep 2 at 6:41
What is "rect"?
â Lord Shark the Unknown
Sep 2 at 6:41
Then I'd say that both "rect" and the second line of your calculation are unnecessary.
â Lord Shark the Unknown
Sep 2 at 6:55
Then I'd say that both "rect" and the second line of your calculation are unnecessary.
â Lord Shark the Unknown
Sep 2 at 6:55
add a comment |Â
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What is "rect"?
â Lord Shark the Unknown
Sep 2 at 6:41
Then I'd say that both "rect" and the second line of your calculation are unnecessary.
â Lord Shark the Unknown
Sep 2 at 6:55