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Abstract
A new fast algorithm is proposed here to compute the discrete Hartley transform (DHT) via the natural-ordered Walsh-Hadamard transform. The processing is carried out on an intraframe basis in (N × N) data blocks, where N is an integer power of 2. The Walsh-Hadamard transform (WHT)W coefficients are computed directly, and then used to obtain the DHT coefficients. This is achieved by an (N × N) transformation matrix (H transform matrix) which is orthonormal and has a block-diagonal structure. As such, it results in substantial saving in the number of multiplications required to obtain the DHT, relative to direct computation. Its total operation is almost equal to that of fast radix 2 DHT, but with a much more simple data transfer path. Using the binary fraction technique, we could get the result within 3 significant digits. The simple, regular and high immunity of round-off noise properties make it practical to be used in signal processing. Above all, it provides a good conversion for these two useful transformations.