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

We propose a computationally efficient approximation for numerically evaluating 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 when M is moderately large. The algorithm is based on the fact that the Hartley transform of a uniformly sampled signal at an arbitrary frequency can be expressed as a weighted sum of the discrete Hartley transform (DHT) coefficients of the signal. Since some summation terms have little effects on the results, a few dominant terms are chosen such that the error of approximation does not exceed the specified limit. We show that for a moderately large M, the proposed algorithm is more efficient than the directly computing method. The computational complexity of the algorithm and its error behavior with white noise and sinusoidals are also described in this paper.