Modified fermat transforms for reliable and efficient de-noising of speech signals

Recently the Modified Fermat Number Transform (MFNT) based on Right-angle circular convolution (RCC) was extended to form a quadratic MFNT (QMFNT) by introducing Left-angle circular convolution (LCC) and interpreting the result as a quadratic representation of the convolution output. A similar concept was then extended to create a Modified Discrete Fourier Transform (MDFT). Both the QMFNT and the MDFT enable efficient convolution (correlation) without zero padding, resulting in improved computational efficiency. This paper investigates the use of the QMFNT and MDFT to implement an efficient novel speech de-noising algorithm that has potential applications for speech enhancement and speech recognition.