A new realization of a digital filter using a number theory transform
Takafumi Edanami, Shigeo Tsujii · Electronics and Communications in Japan (Part I Communications) · 1981
Abstract With the number theory transform it is possible to perform a high‐speed convolution operation without multiplication and without numerical errors. For this reason, applications of the number theory transform to FIR digital filters have drawn attention. However, when the number theory transform is applied to digital filters, the operating word length becomes extremely large to prevent overflow at the output and this becomes a serious problem in actual hardware implementation. A method is proposed for expanding the dynamic range of the input and output in which the higher order difference of the impulse response is made another impulse response. It is shown that the proposed technique can greatly expand the input and output dynamic ranges. The method can also be combined with other techniques to improve its effectiveness.