Leakage analysis and Its application in calculating a sinusoidal parameters

Spectrum leakage is frequently the most effective factor that leads to a considerable error in estimating signal parameters. In our work, an investigation is conducted that how DFT calculations distributed over the leakage spectrum of a sinusoid depends on the length of a windowed sinusoid. It is found that the leakage variation with a sinusoid length can be expressed by a sinc function, which connects DFT calculations with the amplitude, period of a single frequency signal and the length of the windowed sinusoid. Finally, an accurate approach is proposed that can theoretically immune to the leakage effect. The conclusions suggest a new expression for a sinusoid, disclose the leakage law and may lead to some potential applications in DSP.