Notes on Recursive FFT (Fast Fourier Transform) algorithm Fall ...

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(10) The pseudocode for FFT (recursive version) from Cormen, Leisserson, et al, is:

FFT (a) { // 1D array a = (a 0 , a 1 , … , a n-1 )

1 n = length (a) // n is a power of 2

2. if (n == 1)

3. return a

4. ω n = e 2πi/n 1

// ω n

5. ω = 1

6. a [0] = (a 0 , a 2 , a 4 , … a n-2 )

7. a [1] = (a 1 , a 3 , a 5 , … a n-1 )

8. y [0] = FFT(a [0] )

9. y [1] = FFT(a [1] )

10. for (k=0; k

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(10) The pseudocode for FFT (recursive version) from Cormen, Leisserson, et al, is: FFT (a) { // 1D array a = (a 0 , a 1 , … , a n-1 ) 1 n = length (a) // n is a power of 2 2. if (n == 1) 3. return a 4. ω n = e 2πi/n 1 // ω n 5. ω = 1 6. a [0] = (a 0 , a 2 , a 4 , … a n-2 ) 7. a [1] = (a 1 , a 3 , a 5 , … a n-1 ) 8. y [0] = FFT(a [0] ) 9. y [1] = FFT(a [1] ) 10. for (k=0; k

3 Fall 2010

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Page 5: 5 Fall 2010

Notes on Recursive FFT (Fast Fourier Transform) algorithm Fall ...

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