A new digital filter for phasor computation. Part I : Theory

A new pair of orthogonal filters for phasor computation is presented. They have excellent time-frequency characteristics for fault location and measurement. Their impulse responses are obtained applying the inverse Fourier transform to a single-lobe function with a strong stopband. From this process, a new window emerges. Without side lobes, it overcomes the temporal barriers imposed by the rectangular window, implicit in digital Fourier filtering. Its length is not restricted to a multiple of one cycle, and it can be adjusted to cover totally the available samples of the fault, extracting the fundamental component with growing precision. On the other hand, its sampling frequency can be reduced to twice the fundamental frequency. In particular, at this minimum sampling frequency, the digital Cosine filter rejects the even harmonics and the aperiodic component.