Space-Time Wireless Channels

Appendix B. Fourier Analysis

Basic Fourier concepts may not be difficult for a seasoned engineer, but hard-core analysis and calculation is rife with difficulties due to the numerous transform conventions that exist in the literature. In the field of space–time channel modeling, this problem is exacerbated by joint analysis of two or more pairs of spectral domains. Conventions, however, are purely mathematical and can be overcome by keeping a few simple rules in mind. This section is intended to be a recipe book for defining, calculating, and manipulating Fourier transform pairs regardless of their defined conventions. The results will assist analysis in spectral domains such as the time–frequency, time–Doppler, frequency–delay, position–wavenumber, ...