Fourier transform and its applications (Part 2)

This second part of the Fourier transform presentation comprises two separate, unrelated paragraphs. It is based on the developments given in the first part in .

In the first paragraph, we'll look at Fourier transform expressions in the case of digital processing of sampled signals (the discrete Fourier transform), describing the fast Fourier transform algorithm in particular and noting a few practical considerations that shouldn't be overlooked when implementing and using the discrete Fourier transform. We will mention important applications such as MP3 compression of music signals or OFDM modulation used, for example, in digital broadcasting. We also present the main results concerning spectral analysis of random signals, mainly the notions of autocorrelation function and spectral density.

In a second section, we look at the case of two-dimensional signals (most often images) and their representation in frequencies, which will serve as a basis for various fields of application: image compression, image filtering, pre-processing for pattern recognition, with particular reference to the important properties of the Radon transform, which is widely used in medical imaging.

Implementation and application examples will be discussed in a third section. .