Let's look at some important FOURIER pairs, i.e., f(t) and F(o) 1)square function- sinc function Square Sinc for(0<t<τ A[Sin(oτ)/(O] t( Since normal rf pulses are square shaped(in the time domain), their excitation profile (in the frequency domain) is given by its FOURIER transform, the sinc function(approximation for B<180%) The excitation band width is proportional to the reciprocal of the pulse duration, pulses must be short enough to keep the"wiggles"outside the range of interest 2)exponential function- Lorentzian function exponentia Lorentzian t( ν(Hz)17 Let's look at some important FOURIER pairs, i.e., f(t) and F(w): 1) square function — sinc function Since normal rf pulses are square shaped (in the time domain), their excitation profile (in the frequency domain) is given by its FOURIER transform, the sinc function (approximation for b«180°). The excitation band width is proportional to the reciprocal of the pulse duration, pulses must be short enough to keep the "wiggles" outside the range of interest. 2) exponential function — Lorentzian function exponential Lorentzian Square A for (0 < t < ) t Sinc A[sin(wt)/(wt)]