用线性变换和模算法降低离散卷积的复杂度

M. Wintermantel, E. Luder
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引用次数: 0

摘要

对于具有Toeplitz系数矩阵的离散卷积,利用线性变换的方法导出了一种乘法次数最少的一般算法。为了使结果适用于有限字长的长卷积,引入了模算法和块划分。所得算法复杂度小,不产生舍入噪声。这同样适用于线性和循环卷积算法,这些算法是由更一般的Toeplitz卷积算法推导出来的。与基于数论变换的同类算法相比,新算法的主要优点是推导更简单、更一般,对卷积长度的限制更少。
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Reducing the complexity of discrete convolutions by a linear transformation and modulo arithmetic
For the discrete convolution with a Toeplitz coefficient matrix, a general algorithm with minimum number of multiplications is derived by means of a linear transformation. In order to keep the results applicable to long convolutions with limited wordlength, modulo arithmetic and block-partitioning is introduced. The resulting algorithms reveal small complexity and generate no roundoff noise. The same holds for linear and cyclic convolution algorithms derived from the presented algorithms of the more general Toeplitz convolution. The main advantages of the new algorithms compared to similar algorithms based on number theoretic transforms are a simpler and more general derivation and far less restrictions for the convolution length.
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