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## Re: Two-dimensional fft

**From**: |
Laurent Jacques |

**Subject**: |
Re: Two-dimensional fft |

**Date**: |
Fri, 13 Dec 2002 10:41:41 +0100 |

**User-agent**: |
KMail/1.4.3 |

On Friday 13 December 2002 05:28, Richard Morey wrote:
| How does one interpret the output from a two-dimensional fft? I
| understand the interpretation of the one-dimensional fft and fftshift,
| but how does one interpret the matrix of values from a two-dimensional
| fft?
1D FFT -> coefficients of the decomposition of a signal in a sum of 1D
oscillatory functions (complex exponentials) each one specified by one
scalar, the frequency.
2D FFT -> coefficients of the decomposition of an image in a sum of 2D
oscillatory functions (complex exponentials) each speciefied by one vector,
the frequency vector. Thus, the 2D FFT have to be a matrix.
1D FFTSHIFT -> turns the frequency domain [0 2pi/T[ (Where T is the sampling
period) into the centered frequency domain [-pi/T pi/T[ by flipping the
second half part of the vector with the first one.
2D FFTSHIFT -> turns the 2D frequency domain [0 2pi/T]*[0 2pi/T'] (where T and
T' are respectively the sampling period according columns and rows) into the
2D centered frequency domain [-pi/T pi/T[*[-pi/T' pi/T'[ by flipping the
quadrans I and III, and II and IV of the matrix.
Hoping this help,
Laurent.
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