Multi-Dimensional Imaging with Synthetic Aperture Radar

Appendix A: Appendices

A.1 Fourier Transform and properties

The Fourier Transform (FT) is a mathematical transformation that breaks a function into an alternative representation characterized by the sine and cosine functions at varying frequencies. The Fourier Transform shows that any function can be reformulated as the sum of sine waves with variable frequencies, thus allowing representing a signal from its original, space or time domain, into the dual frequency domain. The Fourier Transform originates from the theory of Fourier series which states that any real deterministic periodic function $x(t)$ with period T can be expressed as the discrete ...