Re: Two-dimensional fft

[Laurent Jacques]

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.



-------------------------------------------------------------
Octave is freely available under the terms of the GNU GPL.

Octave's home on the web:  http://www.octave.org
How to fund new projects:  http://www.octave.org/funding.html
Subscription information:  http://www.octave.org/archive.html
-------------------------------------------------------------