  In this paper, we focus on Fourier analysis and holographic transforms for
signal representation. For instance, in the case of image processing, the
holographic representation has the property that an arbitrary portion of the
transformed image enables reconstruction of the whole image with details
missing. We focus on holographic representation defined through the Fourier
Transforms. Thus, We firstly review some results in Fourier transform and
Fourier series. Next, we review the Discrete Holographic Fourier Transform
(DHFT) for image representation. Then, we describe the contributions of our
work. We show a simple scheme for progressive transmission based on the DHFT.
Next, we propose the Continuous Holographic Fourier Transform (CHFT) and
discuss some theoretical aspects of it for 1D signals. Finally, some testes are
presented in the experimental results
