Faster than Fast Fourier Transform?
Is it possible to make an algorithm faster than the fast Fourier transform to calculate the discrete Fourier transform (is there proofs for or against it)?
OR, a one that only approximates the discrete Fourier transform, but is faster than $O(NlogN)$ and still gives about reasonable results?
Additional requirements:
1) Let's leave the quantum computing out
2) I don't mean faster in sense of how its implemented for some specific hardware, but in the "Big-O notation sense", that it would ran e.g. in linear time.
Sorry for my english
fourier-analysis fourier-series
asked Nov 20 '12 at 20:00
just
264
|
show 3 more comments
Is it possible to make an algorithm faster than the fast Fourier transform to calculate the discrete Fourier transform (is there proofs for or against it)?
OR, a one that only approximates the discrete Fourier transform, but is faster than $O(NlogN)$ and still gives about reasonable results?
Additional requirements:
1) Let's leave the quantum computing out
2) I don't mean faster in sense of how its implemented for some specific hardware, but in the "Big-O notation sense", that it would ran e.g. in linear time.
Sorry for my english
fourier-analysis fourier-series
asked Nov 20 '12 at 20:00
just
264
Quantum Fourier Transform: $O(log^2 N)$
– draks ...
Nov 20 '12 at 20:01
Fastest currently implemented algorithm is fftw: fastest Fourier transform in the west. It's $O(nlog n)$ though.
– icurays1
Nov 20 '12 at 20:07
Mmm, ok, additional requirement: one that could be ran on computers we have today. :)
– just
Nov 20 '12 at 20:07
This seems in the right direction.
– WimC
Nov 20 '12 at 20:16
You've seen the Wikipedia page? "All known FFT algorithms require $Theta(N log N)$ operations... although there is no known proof that a lower complexity score is impossible." It would be interesting if we find out that Wikipedia is out of date, of course.
– Rahul
Nov 20 '12 at 20:24
|
show 3 more comments
Is it possible to make an algorithm faster than the fast Fourier transform to calculate the discrete Fourier transform (is there proofs for or against it)?
OR, a one that only approximates the discrete Fourier transform, but is faster than $O(NlogN)$ and still gives about reasonable results?
Additional requirements:
1) Let's leave the quantum computing out
2) I don't mean faster in sense of how its implemented for some specific hardware, but in the "Big-O notation sense", that it would ran e.g. in linear time.
Sorry for my english
fourier-analysis fourier-series
asked Nov 20 '12 at 20:00
just
264
Is it possible to make an algorithm faster than the fast Fourier transform to calculate the discrete Fourier transform (is there proofs for or against it)?
OR, a one that only approximates the discrete Fourier transform, but is faster than $O(NlogN)$ and still gives about reasonable results?
Additional requirements:
1) Let's leave the quantum computing out
2) I don't mean faster in sense of how its implemented for some specific hardware, but in the "Big-O notation sense", that it would ran e.g. in linear time.
Sorry for my english
fourier-analysis fourier-series
fourier-analysis fourier-series
asked Nov 20 '12 at 20:00
just
264
asked Nov 20 '12 at 20:00
just
264
edited Nov 20 '12 at 20:13
asked Nov 20 '12 at 20:00
just
264
asked Nov 20 '12 at 20:00
just
264
asked Nov 20 '12 at 20:00
just
264
264
Quantum Fourier Transform: $O(log^2 N)$
– draks ...
Nov 20 '12 at 20:01
Fastest currently implemented algorithm is fftw: fastest Fourier transform in the west. It's $O(nlog n)$ though.
– icurays1
Nov 20 '12 at 20:07
Mmm, ok, additional requirement: one that could be ran on computers we have today. :)
– just
Nov 20 '12 at 20:07
This seems in the right direction.
– WimC
Nov 20 '12 at 20:16
You've seen the Wikipedia page? "All known FFT algorithms require $Theta(N log N)$ operations... although there is no known proof that a lower complexity score is impossible." It would be interesting if we find out that Wikipedia is out of date, of course.
– Rahul
Nov 20 '12 at 20:24
|
show 3 more comments
Quantum Fourier Transform: $O(log^2 N)$
– draks ...
Nov 20 '12 at 20:01
Fastest currently implemented algorithm is fftw: fastest Fourier transform in the west. It's $O(nlog n)$ though.
– icurays1
Nov 20 '12 at 20:07
Mmm, ok, additional requirement: one that could be ran on computers we have today. :)
– just
Nov 20 '12 at 20:07
This seems in the right direction.
– WimC
Nov 20 '12 at 20:16
You've seen the Wikipedia page? "All known FFT algorithms require $Theta(N log N)$ operations... although there is no known proof that a lower complexity score is impossible." It would be interesting if we find out that Wikipedia is out of date, of course.
– Rahul
Nov 20 '12 at 20:24
Quantum Fourier Transform: $O(log^2 N)$
– draks ...
Nov 20 '12 at 20:01
Quantum Fourier Transform: $O(log^2 N)$
– draks ...
Nov 20 '12 at 20:01
Fastest currently implemented algorithm is fftw: fastest Fourier transform in the west. It's $O(nlog n)$ though.
– icurays1
Nov 20 '12 at 20:07
Fastest currently implemented algorithm is fftw: fastest Fourier transform in the west. It's $O(nlog n)$ though.
– icurays1
Nov 20 '12 at 20:07
Mmm, ok, additional requirement: one that could be ran on computers we have today. :)
– just
Nov 20 '12 at 20:07
Mmm, ok, additional requirement: one that could be ran on computers we have today. :)
– just
Nov 20 '12 at 20:07
This seems in the right direction.
– WimC
Nov 20 '12 at 20:16
This seems in the right direction.
– WimC
Nov 20 '12 at 20:16
You've seen the Wikipedia page? "All known FFT algorithms require $Theta(N log N)$ operations... although there is no known proof that a lower complexity score is impossible." It would be interesting if we find out that Wikipedia is out of date, of course.
– Rahul
Nov 20 '12 at 20:24
You've seen the Wikipedia page? "All known FFT algorithms require $Theta(N log N)$ operations... although there is no known proof that a lower complexity score is impossible." It would be interesting if we find out that Wikipedia is out of date, of course.
– Rahul
Nov 20 '12 at 20:24
|
show 3 more comments
1 Answer
1
active
oldest
votes
There is an algorithm called sparse fast Fourier transform (sFFT), which is faster than FFT algorithms when the Fourier coefficients are sparse.
answered Nov 20 '12 at 21:17
chaohuang
3,20421529
This appears to be partly the same that was pointed out by WimC (the paper he mentions could be found from the page you provided). I will accept your answer. Thanks also for WimC!
– just
Nov 20 '12 at 22:05
add a comment |
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1 Answer
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1 Answer
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oldest
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votes
There is an algorithm called sparse fast Fourier transform (sFFT), which is faster than FFT algorithms when the Fourier coefficients are sparse.
answered Nov 20 '12 at 21:17
chaohuang
3,20421529
This appears to be partly the same that was pointed out by WimC (the paper he mentions could be found from the page you provided). I will accept your answer. Thanks also for WimC!
– just
Nov 20 '12 at 22:05
add a comment |
There is an algorithm called sparse fast Fourier transform (sFFT), which is faster than FFT algorithms when the Fourier coefficients are sparse.
answered Nov 20 '12 at 21:17
chaohuang
3,20421529
This appears to be partly the same that was pointed out by WimC (the paper he mentions could be found from the page you provided). I will accept your answer. Thanks also for WimC!
– just
Nov 20 '12 at 22:05
add a comment |
There is an algorithm called sparse fast Fourier transform (sFFT), which is faster than FFT algorithms when the Fourier coefficients are sparse.
answered Nov 20 '12 at 21:17
chaohuang
3,20421529
There is an algorithm called sparse fast Fourier transform (sFFT), which is faster than FFT algorithms when the Fourier coefficients are sparse.
answered Nov 20 '12 at 21:17
chaohuang
3,20421529
answered Nov 20 '12 at 21:17
chaohuang
3,20421529
answered Nov 20 '12 at 21:17
chaohuang
3,20421529
answered Nov 20 '12 at 21:17
chaohuang
3,20421529
3,20421529
This appears to be partly the same that was pointed out by WimC (the paper he mentions could be found from the page you provided). I will accept your answer. Thanks also for WimC!
– just
Nov 20 '12 at 22:05
add a comment |
This appears to be partly the same that was pointed out by WimC (the paper he mentions could be found from the page you provided). I will accept your answer. Thanks also for WimC!
– just
Nov 20 '12 at 22:05
This appears to be partly the same that was pointed out by WimC (the paper he mentions could be found from the page you provided). I will accept your answer. Thanks also for WimC!
– just
Nov 20 '12 at 22:05
This appears to be partly the same that was pointed out by WimC (the paper he mentions could be found from the page you provided). I will accept your answer. Thanks also for WimC!
– just
Nov 20 '12 at 22:05
add a comment |
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Quantum Fourier Transform: $O(log^2 N)$
– draks ...
Nov 20 '12 at 20:01
Fastest currently implemented algorithm is fftw: fastest Fourier transform in the west. It's $O(nlog n)$ though.
– icurays1
Nov 20 '12 at 20:07
Mmm, ok, additional requirement: one that could be ran on computers we have today. :)
– just
Nov 20 '12 at 20:07
This seems in the right direction.
– WimC
Nov 20 '12 at 20:16
You've seen the Wikipedia page? "All known FFT algorithms require $Theta(N log N)$ operations... although there is no known proof that a lower complexity score is impossible." It would be interesting if we find out that Wikipedia is out of date, of course.
– Rahul
Nov 20 '12 at 20:24