For realistic durations, the divergences and convergences are less extreme, and smaller non-zero convergences (spectral leakage) appear at many other frequencies, but the concept of negative frequency still applies. Fourier 's original formulation (the sine transform and the cosine transform) requires an integral for the cosine and another for the sine. And the resultant trigonometric expressions are often less tractable than complex exponential expressions. (see Analytic signal, Euler's formula § Relationship to trigonometry, and Phasor)