Modified Discrete Fourier Transforms for fast convolution and adaptive filtering

Recently the previously reported Modified Fermat Number Transform (MFNT) based on Right Circular Convolution (RCC) was extended to form a Quadratic MFNT (QMFNT) by introducing Left-angle Circular Convolution (LCC) and interpreting the combined result as a quadratic representation of the resulting convolution output. This paper introduces a new Modified Discrete Fourier Transform (MDFT) that relies on a similar combination of RCC and LCC. The MDFT enables overlap-add FFT block processing to be implemented without zero padding, resulting in reduced computational complexity and potentially reduced power requirements in nanoscale VLSI implementations.