Design of Convolution Window Based on All-phase Filtering

The frequency sampling theorem of the full-phase digital filter is derived theoretically, and the conclusion that the system characteristics pass through the frequency sampling point and the double window conditions are lower than the sampling point is proved. Based on rectangular Windows, Bartlett, Cosine, Hanning, Hamming, Blackman, and Papoulis, the transition band widths, minimum side lobe attenuation, and side lobe attenuation speeds of full-phase single and double window convolution windows are given. On this basis, this paper proposes a new method to construct the window function according to the least squares criterion, and theoretically deduces the arithmetic expression of the window function. In the experiment, on the amplitude frequency characteristic function of the full-phase digital filter, the minimum error base window is designed by the least square method. Compared with the Bartlett base window, the error is reduced by 2 % and the transition band is reduced by 6.9 dB.