Fourier transforms

is a table with functions of time \(f(t)\) on the left and corresponding Fourier transforms \(F(\omega)\) on the right. Where applicable, \(T\) is the time-domain period, \(\omega_0 2\pi/T\) is the corresponding angular frequency, \(j = \sqrt{-1}\), \(a \in \mathbb{R}^+\), and \(b, t_0 \in \mathbb{R}\) are constants. Furthermore, \(f_e\) and \(f_0\) are even and odd functions of time, respectively, and it can be shown that any function \(f\) can be written as the sum \(f(t) = f_e(t) + f_0(t)\). (Hsu 1970,appendix E)