Quadratic Modified Fermat Transforms for fast convolution and adaptive filtering

Previously it was shown that the Modified Fermat Number Transform (MFNT) reduces computational requirements for an adaptive filter architecture based on convolution achieved by FNT block processing (FNTBP). The work of this paper extends the MFNT to a Quadratic MFNT (QMFNT) by introducing Left-angle circular convolution and interpreting the result as a quadratic representation of the convolution output obtained by combining the Left-angle and Right-angle circular convolutions. The resulting computational complexity is similar to the MFNT but provides a significant reduction of the dynamic range constraints on the input sequences. This results in an adaptive filter architecture that has increased computational efficiency and potentially lower power requirements when used to realize nano-scale adaptive filters.