Hartley series and notch Hartley transform

A new class of Hartley transform is introduced—the Hartley series (HS). The Hartley series is appropriate in the situation that the input signal is continuous and periodic in time, and hence its Hartley transform is discrete in frequency. Through this class of Hartley transform, any continuous and periodic signal can be decomposed into the weighted sum of cas functions (where cas (·) = cos (·) + sin (·)) In order to compute these Hartley coefficients, an algorithm referred to as the notch Hartley transform (NHT) is also presented. This algorithm can be applied to the input signal composed of arbitrary frequencies, and all Hartley coefficients can be computed in advance of the end of one period of the signal