The Discrete Hirschman Transform (DHT) is a generalization of the entropy-based Hirschman Transform that canonically represents digital signals with sparse basis functions. The DHT is computationally attractive in providing the flexibility in hardware implementations since it has a sparse structure that is similar to that of the Discrete Fourier Transform (DFT) basis. This Hirschman-based algorithm has been widely applied in many digital signal processing algorithms such as denoising, filtering, and linear convolution. In this paper, we have developed two fast algorithms: the radix-2 and radix-4 DHT algorithms. These efficient algorithms significantly reduce the number of nontrivial real computations when compared to the original DHT algorithm and other popular Fast Fourier Transforms (FFTs). We show that it is feasible to realize our new algorithms in hardware through the use of a repetitive application of butterfly computations in a structure that will be familiar to those already working with the similar FFT algorithms. Our proposed algorithms reduce the number of nontrivial real computations while efficiently using available hardware resources.

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关于计算离散赫希曼变换


离散赫希曼变换 (DHT) 是基于熵的赫希曼变换的推广，它规范地表示具有稀疏基函数的数字信号。 DHT 在提供硬件实现灵活性方面在计算上很有吸引力，因为它具有类似于离散傅立叶变换 (DFT) 基础的稀疏结构。这种基于赫希曼的算法已广泛应用于去噪、滤波、线性卷积等许多数字信号处理算法中。在本文中，我们开发了两种快速算法：radix-2 和 radix-4 DHT 算法。与原始 DHT 算法和其他流行的快速傅立叶变换 (FFT) 相比，这些高效算法显着减少了重要的实际计算数量。我们证明，通过在已经使用类似 FFT 算法的人员所熟悉的结构中重复应用蝶形计算，在硬件中实现我们的新算法是可行的。我们提出的算法减少了重要的实际计算的数量，同时有效地使用可用的硬件资源。