A Computationally Efficient DFT Scheme for Applications With a Subset of Nonzero Inputs

Fourier transformation is a powerful analytical tool with wide-ranging applications in many fields. In certain cases, some of the inputs to the transformation function are zero, while the others are real or complex. For the case, where the nonzero inputs are complex, the transform decomposition (TD) method enables a significant reduction in the computational complexity. This letter proposes a modified TD (MTD) algorithm to further reduce the complexity when the nonzero input data are consecutive and real-valued. The analytical and numerical results confirm that the complexity of the MTD scheme is not only significantly lower than that of the original TD method, but also lower than that of the traditional split-radix fast Fourier transform (FFT) method when the length of the input sequence is short.