Proof of Poisson Summation Formula [closed]
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In the proof of Poisson Summation Formula as presented in the text book Fourier Analysis:
enter image description here
I understand a variable change of y=x+n was made, but then how come x in the power of e became y and not (y-n)
fourier-analysis
asked Dec 13 '18 at 2:31
Naji ANaji A
1
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closed as off-topic by Saad, KReiser, Cesareo, José Carlos Santos, TZakrevskiy Dec 13 '18 at 9:37
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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, KReiser, Cesareo, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
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$begingroup$
In the proof of Poisson Summation Formula as presented in the text book Fourier Analysis:
enter image description here
I understand a variable change of y=x+n was made, but then how come x in the power of e became y and not (y-n)
fourier-analysis
asked Dec 13 '18 at 2:31
Naji ANaji A
1
$endgroup$
closed as off-topic by Saad, KReiser, Cesareo, José Carlos Santos, TZakrevskiy Dec 13 '18 at 9:37
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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, KReiser, Cesareo, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
$begingroup$
In the proof of Poisson Summation Formula as presented in the text book Fourier Analysis:
enter image description here
I understand a variable change of y=x+n was made, but then how come x in the power of e became y and not (y-n)
fourier-analysis
asked Dec 13 '18 at 2:31
Naji ANaji A
1
$endgroup$
In the proof of Poisson Summation Formula as presented in the text book Fourier Analysis:
enter image description here
I understand a variable change of y=x+n was made, but then how come x in the power of e became y and not (y-n)
fourier-analysis
fourier-analysis
asked Dec 13 '18 at 2:31
Naji ANaji A
1
asked Dec 13 '18 at 2:31
Naji ANaji A
1
asked Dec 13 '18 at 2:31
Naji ANaji A
1
asked Dec 13 '18 at 2:31
Naji ANaji A
1
asked Dec 13 '18 at 2:31
Naji ANaji A
1
1
closed as off-topic by Saad, KReiser, Cesareo, José Carlos Santos, TZakrevskiy Dec 13 '18 at 9:37
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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, KReiser, Cesareo, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
closed as off-topic by Saad, KReiser, Cesareo, José Carlos Santos, TZakrevskiy Dec 13 '18 at 9:37
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 provide additional context, which ideally explains why the question is relevant to you and our community. Some forms of context include: background and motivation, relevant definitions, source, possible strategies, your current progress, why the question is interesting or important, etc." – Saad, KReiser, Cesareo, José Carlos Santos
If this question can be reworded to fit the rules in the help center, please edit the question.
add a comment |
add a comment |
1 Answer
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$e^{-2pi (y-k)}=e^{-2pi iy}e^{-2pi ik} = e^{-2pi iy}$
$e^{-2pi ik} = 1$ for integers $k$
answered Dec 13 '18 at 2:37
Bernard WBernard W
1,521612
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Absolutely right! Thanks a lot.
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– Naji A
Dec 14 '18 at 2:35
add a comment |
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
$begingroup$
$e^{-2pi (y-k)}=e^{-2pi iy}e^{-2pi ik} = e^{-2pi iy}$
$e^{-2pi ik} = 1$ for integers $k$
answered Dec 13 '18 at 2:37
Bernard WBernard W
1,521612
$endgroup$
$begingroup$
Absolutely right! Thanks a lot.
$endgroup$
– Naji A
Dec 14 '18 at 2:35
add a comment |
$begingroup$
$e^{-2pi (y-k)}=e^{-2pi iy}e^{-2pi ik} = e^{-2pi iy}$
$e^{-2pi ik} = 1$ for integers $k$
answered Dec 13 '18 at 2:37
Bernard WBernard W
1,521612
$endgroup$
$begingroup$
Absolutely right! Thanks a lot.
$endgroup$
– Naji A
Dec 14 '18 at 2:35
add a comment |
$begingroup$
$e^{-2pi (y-k)}=e^{-2pi iy}e^{-2pi ik} = e^{-2pi iy}$
$e^{-2pi ik} = 1$ for integers $k$
answered Dec 13 '18 at 2:37
Bernard WBernard W
1,521612
$endgroup$
$e^{-2pi (y-k)}=e^{-2pi iy}e^{-2pi ik} = e^{-2pi iy}$
$e^{-2pi ik} = 1$ for integers $k$
answered Dec 13 '18 at 2:37
Bernard WBernard W
1,521612
edited Dec 13 '18 at 5:07
answered Dec 13 '18 at 2:37
Bernard WBernard W
1,521612
answered Dec 13 '18 at 2:37
Bernard WBernard W
1,521612
answered Dec 13 '18 at 2:37
Bernard WBernard W
1,521612
1,521612
$begingroup$
Absolutely right! Thanks a lot.
$endgroup$
– Naji A
Dec 14 '18 at 2:35
add a comment |
$begingroup$
Absolutely right! Thanks a lot.
$endgroup$
– Naji A
Dec 14 '18 at 2:35
$begingroup$
Absolutely right! Thanks a lot.
$endgroup$
– Naji A
Dec 14 '18 at 2:35
$begingroup$
Absolutely right! Thanks a lot.
$endgroup$
– Naji A
Dec 14 '18 at 2:35
add a comment |
