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References

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  1. A. V. Lugt, IEEE Trans. IT10, 139 (1964).
  2. W. K. Pratt, J. Kane, H. C. Andrews, Proc. IEEE 57, 58 (1969).
    [CrossRef]
  3. G. Nagy, IEEE Trans. SSC5, 273 (1969).

1969 (2)

W. K. Pratt, J. Kane, H. C. Andrews, Proc. IEEE 57, 58 (1969).
[CrossRef]

G. Nagy, IEEE Trans. SSC5, 273 (1969).

1964 (1)

A. V. Lugt, IEEE Trans. IT10, 139 (1964).

Andrews, H. C.

W. K. Pratt, J. Kane, H. C. Andrews, Proc. IEEE 57, 58 (1969).
[CrossRef]

Kane, J.

W. K. Pratt, J. Kane, H. C. Andrews, Proc. IEEE 57, 58 (1969).
[CrossRef]

Lugt, A. V.

A. V. Lugt, IEEE Trans. IT10, 139 (1964).

Nagy, G.

G. Nagy, IEEE Trans. SSC5, 273 (1969).

Pratt, W. K.

W. K. Pratt, J. Kane, H. C. Andrews, Proc. IEEE 57, 58 (1969).
[CrossRef]

IEEE Trans. (2)

A. V. Lugt, IEEE Trans. IT10, 139 (1964).

G. Nagy, IEEE Trans. SSC5, 273 (1969).

Proc. IEEE (1)

W. K. Pratt, J. Kane, H. C. Andrews, Proc. IEEE 57, 58 (1969).
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

Fourier transform device.

Fig. 2
Fig. 2

Fourier transform output for input (1, 1, 0, 0, 1, 1, 0, 0, 1): (a) real part; (b) imaginary part. (Theoretical value, —●—; experimental value, ○.)

Equations (9)

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g ( u ) = s f ( x ) h ( u , x ) d x ,
g p = k f k h k p
g p q = k l f k l h k l p q
DFT :             F p = k = - n n f k W - p k             p = - n , - n + 1 , , n IDFT :             f k = ( 1 / N ) p = - n n F p W p k             k = - n , - n + 1 , , n
DFT :             F p q = k = - n n l = - n n f k l W - ( k p + l q ) , IDFT :             f k l = ( 1 / N 2 ) p = - n n q = - n n F p q W k p + l q ,             p , q , k , l = - n , - n + 1 , , n .
Re F p = k = - n n f k [ 1 + cos ( - 2 π p k / N ) ] = F 0 + Re F p , Im F p = k = - n n f k [ 1 + sin ( - 2 π p k / N ) ] = F 0 + Im F p .
Re F p + = k = - n n f k rect [ cos ( - 2 π p k / N ) ] , Re F p - = k = - n n f k rect [ - cos ( - 2 π p k / N ) ] , Im F p + = k = - n n f k rect [ sin ( - 2 π p k / N ) ] , Im F p - = k = - n n f k rect [ - sin ( - 2 π p k / N ) ] ,
rect ( x ) = { 0 x < 0. x x 0.
Re F p = Re F p + - Re F p - , Im F p = Im F p + - Im F p - .

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