Looking at the first term of this result, when ω ω = ω ω 1 , the negative frequency − − ω ω 1 cancels the positive frequency, leaving just the constant coefficient A 1 (because e i 0 t = e 0 = 1 ), which causes the infinite integral to diverge. At other values of ω ω the residual oscillations cause the integral to converge to zero. This idealized Fourier transform is usually written as: