任意長(zhǎng)度離散Hartley變換的快速算法
FAST ALGORITHMS FOR DISCRETE HARTLEY TRANSFORM OF ARBITRARY LENGTH
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摘要: 本文把長(zhǎng)為plq(p為奇數(shù),q為任意自然數(shù))的DHT轉(zhuǎn)化為Pl個(gè)長(zhǎng)為q的DHT的計(jì)算及其附加運(yùn)算,附加運(yùn)算只涉及P點(diǎn)cos-DFT和sin-DFT的計(jì)算;對(duì)長(zhǎng)度(P1l,1,Psls 2l (p1, , ps為奇素?cái)?shù))的DHT,用同樣的遞歸技術(shù)得到其快速算法,因而可計(jì)算任意長(zhǎng)度的DHT;文中還論證了計(jì)算長(zhǎng)為N的DHT所需的乘法和加法運(yùn)算量不超過(guò)O(Nlog2N)。當(dāng)長(zhǎng)度為N=pl時(shí),本文算法的乘法量比其他已知算法更少。
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關(guān)鍵詞:
- 信號(hào)處理; Hartley變換; 快速算法
Abstract: DHT of length plq (p is odd. q is arbitrary) is turned into p-DHT's of length q and some additional operations while the additional operations only invol ves the computation of cos-DFT and sin-DFT with length p. If the length of a DHT is p1l1psls2l)(p1,, ps are odd primes), a fast algorithm is obtained by the similar recursive technique. Therefore, the algorithm can compute DHT of arbitrary length. The paper also proves that operations for computing DHT of length N by the algorithm are no more than O(Nlog2N). When the length is N=pl, operations of the algorithm are less than that of other known algorithms. -
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