A new convolutional and deconvolutional method

The linear convolution and deconvolution are often changed to the circulant convolution and deconvolution with k = 1 before they are computed by the use of the FFT method.Correspondingly,the expected results can only be approximate.In this paper,we propose a new method by changing the linear convolution and deconvolution to k=±(-1)~(1/2) circulant convolution and deconvolution.Then the linear convolution can be correct without any additional computation while the edge effect can be greatly reduced within the result of he linear deconvolution.