FAST HIGH-RESOLUTION APPROXIMATION OF THE HARTLEY TRANSFORM AT ARBITRARY FREQUENCIES

We propose a computationally efficient approximation for numerically e valuating the Hartley transform at arbitrary frequencies of a sequence . By use of this algorithm, one can efficiently calculate the Hartley transform of a sequence of length N at arbitrary M frequency points wh en M is moderately large. The algorithm is based on the fact that the Hartley transform of a uniformly sampled signal at an arbitrary freque ncy can be expressed as a weighted sum of the discrete Hartley transfo rm (DHT) coefficients of the signal. Since some summation terms have l ittle effects on the results, a few dominant terms are chosen such tha t the error of approximation does not exceed the specified limit. We s how that for a moderately large M, the proposed algorithm is more effi cient than the directly computing method. The computational complexity of the algorithm and its error behavior with white noise and sinusoid als are also described in this paper.