Fast computation of discrete Hartley transform via Walsh–Hadamard transform

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Fast computation of discrete Hartley transform via Walsh–Hadamard transform

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A new fast algorithm is proposed to compute the discrete Hartley transform (DHT) via the Walsh–Hadamard transform (WHT). The processing is carried out on an interframe basis in (N × N) data blocks, where N is an integer power of two. The WHT coefficients are obtained directly, and then used to obtain the DHT coefficients. This is achieved by a transform matrix, the H-transform matrix, which is ortho-normal and has a block-diagonal structure. A complete derivation of the block-diagonal structure for the H-transform matrix is given.

Inspec keywords: computerised signal processing; transforms; computational complexity

Other keywords: DHT; fast computation; interframe basis; computational complexity; derivation; fast algorithm; Walsh-Hadamard transform; orthonormal matrix; WHT; discrete Hartley transform; parallel processing; H-transform matrix; block-diagonal structure

Subjects: Programming and algorithm theory; Numerical analysis; Communications computing; Other numerical methods; Other numerical methods; Signal processing and detection

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