On Computing the Discrete Hartley Transform

Henrik V. Sorensen, Douglas L. Jones, C. Sidney Burrus, Michael T. Heideman

Research output: Contribution to journalArticlepeer-review


The discrete Hartley transform (DHT) is a real-valued transform closely related to the DFT of a real-valued sequence. Bracewell has recently demonstrated a radix-2 decimation-in-time fast Hartley transform (FHT) algorithm. In this paper a complete set of fast algorithms for computing the DHT is developed, including decimation-in-frequency, radix-4, split radix, prime factor, and Winograd transform algorithms. The philosophies of all common FFT algorithms are shown to be equally applicable to the computation of the DHT, and the FHT algorithms closely resemble their FFT counterparts. The operation counts for the FHT algorithms are determined and compared to the counts for corresponding real-valued FFT algorithms. The FHT algorithms are shown to always require the same number of multiplications, the same storage, and a few more additions than the real-valued FFT algorithms. Even though computation of the FHT takes more operations, in some situations the inherently real-valued nature of the discrete Hartley transform may justify this extra cost.

Original languageEnglish (US)
Pages (from-to)1231-1238
Number of pages8
JournalIEEE Transactions on Acoustics, Speech, and Signal Processing
Issue number5
StatePublished - Oct 1985
Externally publishedYes

ASJC Scopus subject areas

  • Signal Processing


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