(a) Explain, giving two simple examples, what is meant by the frequency spectrum of a time-dependent wave signal f(). (b) What is meant by the terms Fourier synthesis and Fourier analysis? Indicate how they can be used to understand wave propagation, and under what conditions they may be used. A radio signal, comprising a modulated carrier wave, may be written as Re[f(1)], where: f ( 1) = ale+ azek + age. and 41, d2, d3, w1, wa and why are constant parameters. (c) The frequency spectrum of /() is given by its Fourier transform: F (w) = / five "di. Show that F(w) may be written as: F(w) = ajo(w, - w) + a26(wz -w) + a;o(w; -w) where the Dirac o-function is defined by: 6(y) = edz. (d) Hence determine the average frequency of the power spectrum, defined by: So wF (w)F(w)du So F(w)F(w)du (e) If az and as are small in comparison with a, and the frequencies way, why and wx are similar, show that @ = wi