论文部分内容阅读
近年出现了一种利用数论中的Mobiue函数进行数字信号处理的傅里叶分析技术（通常称为算术博里叶变换）。这种方法在计算离散傅里叶变换时所需乘法次数仅为O(N)且非常适于VLSI处理．本文注意到利用这种技术计算离散余弦变换，只需计算两个博里叶系数中更为简单的偶分量an，从而使得计算N点离散余弦变换的乘法次数仅为N，计算结构相当简单．此外，计算机模拟表明，这种方法的误差与直接计算DCT缃比并不大，可以容忍。
In recent years, a Fourier analysis technique (commonly referred to as arithmetic Fourier transform) has been developed that uses the Mobiue function in number theory for digital signal processing. This method requires only O (N) multiplications to compute the discrete Fourier transform and is well suited for VLSI processing. In this paper, we note that using this technique to calculate discrete cosine transform, we only need to calculate the simple even component an of the two Bohr coefficients so that the N-point discrete cosine transform can only be multiplied by N and the calculation structure is quite simple. In addition, computer simulations show that the error of this method is not large compared with the direct calculation of DCT, which can be tolerated.