Question about roots of unity in the Fast Fourier Transform The Next CEO of Stack...
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Question about roots of unity in the Fast Fourier Transform
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I am learning about the Fast Fourier Transform, which converts a polynomial from its coefficient representation into its point-wise form using divide-and-conquer. The Fast Fourier Transform evaluates a polynomial of degree 'n' at 'n' distinct points. The 'n' distinct points are the 'nth' roots of unity.
I know that a root of unity is a complex number that when raised to some positive integer power 'n' is equal to 1. However, I am not sure what is the advantage of using roots of unity in the Fast Fourier Transform. Any insights are appreciated.
fourier-analysis roots-of-unity fast-fourier-transform
asked Mar 17 at 7:19
ceno980ceno980
455
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add a comment |
$begingroup$
I am learning about the Fast Fourier Transform, which converts a polynomial from its coefficient representation into its point-wise form using divide-and-conquer. The Fast Fourier Transform evaluates a polynomial of degree 'n' at 'n' distinct points. The 'n' distinct points are the 'nth' roots of unity.
I know that a root of unity is a complex number that when raised to some positive integer power 'n' is equal to 1. However, I am not sure what is the advantage of using roots of unity in the Fast Fourier Transform. Any insights are appreciated.
fourier-analysis roots-of-unity fast-fourier-transform
asked Mar 17 at 7:19
ceno980ceno980
455
$endgroup$
add a comment |
$begingroup$
I am learning about the Fast Fourier Transform, which converts a polynomial from its coefficient representation into its point-wise form using divide-and-conquer. The Fast Fourier Transform evaluates a polynomial of degree 'n' at 'n' distinct points. The 'n' distinct points are the 'nth' roots of unity.
I know that a root of unity is a complex number that when raised to some positive integer power 'n' is equal to 1. However, I am not sure what is the advantage of using roots of unity in the Fast Fourier Transform. Any insights are appreciated.
fourier-analysis roots-of-unity fast-fourier-transform
asked Mar 17 at 7:19
ceno980ceno980
455
$endgroup$
I am learning about the Fast Fourier Transform, which converts a polynomial from its coefficient representation into its point-wise form using divide-and-conquer. The Fast Fourier Transform evaluates a polynomial of degree 'n' at 'n' distinct points. The 'n' distinct points are the 'nth' roots of unity.
I know that a root of unity is a complex number that when raised to some positive integer power 'n' is equal to 1. However, I am not sure what is the advantage of using roots of unity in the Fast Fourier Transform. Any insights are appreciated.
fourier-analysis roots-of-unity fast-fourier-transform
fourier-analysis roots-of-unity fast-fourier-transform
asked Mar 17 at 7:19
ceno980ceno980
455
asked Mar 17 at 7:19
ceno980ceno980
455
asked Mar 17 at 7:19
ceno980ceno980
455
asked Mar 17 at 7:19
ceno980ceno980
455
asked Mar 17 at 7:19
ceno980ceno980
455
455
add a comment |
add a comment |
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