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COMPLEX CEPSTRUM OF DISCRETE HARTLEY AND WARPED DISCRETE HARTLEY FILTERS

机译：Complex Cepstrum的离散哈特利和翘曲的离散哈特利过滤器

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摘要

In this paper, we derive the theoretical complex cepstrum (TCC) of the discrete Hartley transform (DHT,[1]) and warped discrete Hartley transform (WDHT) filters. In our derivations, we start with the filter bank structure for the DHT, where each basis is represented by a finite impulse response (FIR) filter. The WDHT filter bank is obtained by substituting z{sup}(-1) in the DHT filter bank with a first-order all-pass filter having β as its coefficient. The value of the β controls the degree and nature of the frequency warping. Here, we choose the value of β, such that the frequency warping follow the psychoacoustic bark scale. Using the filter bank structures, we first derive the transfer functions for the DHT and WDHT, and subsequently the TCC for each filter is computed. We analyze the DHT and WDHT filter transfer functions and the TCC by illustrating the corresponding pole-zero maps. Moreover, we also use the derived TCC expressions to compute the cepstral sequence for a synthetic vowel /aa/ and compare with the discrete cosine and warped-discrete cosine transform cepstral sequences derived in [2].
机译：在本文中，我们得出了离散的Hartley变换（DHT，[1]）和翘曲的离散Hartley变换（WDHT）过滤器的理论复合综合克斯特劳（TCC）。在我们的推导中，我们从DHT的滤波器组结构开始，其中每个基础由有限脉冲响应（FIR）过滤器表示。通过将DHT滤波器组中的z {sup}（ - 1）用具有β作为其系数的一阶All-Pass滤波器来获得WDHT滤波器。 β的值控制频率翘曲的程度和性质。在这里，我们选择β的值，使得频率扭曲遵循心理声学吠声。使用滤波器组结构，我们首先导出DHT和WDHT的传递函数，随后计算每个过滤器的TCC。我们通过说明相应的极零地图来分析DHT和WDHT滤波器传递函数和TCC。此外，我们还使用衍生的TCC表达来计算合成元音/ AA / AA /并与衍生在[2]中的离散余弦和翘曲 - 离散余弦变换倒谱序列的倒谱序列。

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