1. Antenna, linear spatial frequency filter

1.1 The role of the Fourier transform

In general, we will consider signals whose relative frequency bands are sufficiently narrow to be represented by complex numbers or complex vectors characterizing the moduli, phases and polarizations of these signals. Spectral analysis of linear media allows us to deduce their response to a broadband signal from their harmonic responses.

We know that the radiation pattern of an antenna is obtained by Fourier transforming the illumination law of its aperture. Let's take the case of a linear aperture of extent D (that, for example, of a linear array of pitch a, figure 1 ). Let x be the abscissa of a point of this aperture relative to its center...