Fourier transform - Applications (Part 3)

This third part of the Fourier transform presentation builds on the concepts presented in § 2 and on the multidimensional extension of tools described in and in , § 1.

It shows the application of previously developed concepts and deals firstly with problems linked to image sampling, the tools needed for digital image filtering and the spectral analysis of multi-dimensional signals, mentioning a special case, the cosine transform at the basis of image compression techniques. It extends the tools used to study random signals, such as spectral analysis, to two-dimensional signals.

Finally, in a second paragraph, she discusses a few areas where the use of frequency analysis is fundamental, such as wave propagation, the solution of partial differential equations, medical imaging, interferometry and the analysis of contours in an image.