The continuous Fourier transform is defined to be a two-sided Laplace transform with a purely real coefficient such that . D t over a total interval D T . The transform is only applicable within the limits of the so called spectral window. This frequency corresponds to a sine wave of period equal to the whole interval D T . This frequency is a result of the Shannon sampling theorem which states that in order to reconstruct a signal containing frequency components in the spectrum 0 to w m from sampled data, uniformly-spaced samples must be taken at a rate of at least 2 w m .
Spectral leakage is inherent to frequency analysis with a finite amount of data.
Leakage to distant frequencies arises from the finite size of the interval between samples. The shorter the total sampling interval, the more pronounced the sidelobe structure. The use of a data window, or tapering function, is a standard method for reducing sidelobe structures in Fourier transforms. The choice of the tapering function is somewhat arbitrary, but Bingham et al. Unfortunately, the only effect tapering has on the data for this work is to reduce the overall power within the signal, because the sidelobe structures are primarily caused by the irregular spacing.