A digital signal processing (DSP) architecture is presented to compute single bins of the discrete Fourier transform (DFT) with low complexity. This architecture consists of a cascade of simple accumulators working at the input sampling rate and a polyphase finite impulse response (FIR) filter with complex coefficients working at a lower rate. The advantage of this structure is that, for several cases, it is possible to have a system with only one accumulator operating in the high-rate section and a low-order FIR filter working in the low-rate section. However, this depends on the index of the frequency bin to be computed (k) and the number of DFT points (N). Advantages and limitations of this approach are presented, and the implementation scheme is elaborated.

中文翻译：

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简化单仓离散傅里叶变换计算 [提示和技巧]


提出了一种数字信号处理 (DSP) 架构，以低复杂度计算离散傅里叶变换 (DFT) 的单个 bin。该架构由一系列以输入采样率工作的简单累加器和一个以较低速率工作的具有复杂系数的多相有限脉冲响应 (FIR) 滤波器组成。这种结构的优点在于，在某些情况下，可以有一个系统，其中只有一个累加器工作在高速率部分，而一个低阶FIR滤波器工作在低速率部分。然而，这取决于要计算的频率仓的索引（k）和DFT点的数量（N）。介绍了该方法的优点和局限性，并详细阐述了实现方案。