Computing efficiency of the three-stage interpolated low pass filters

Undoubted advantages of finite impulse response filters are their unconditional stability, the absence of limit cycles and the possibility of implementing a filter that does not introduce phase distortion. The disadvantage of such filters is the large cost required to compute the response. This paper considers three-stage interpolated finite impulse response low-pass filters. The maximum values of the interpolation factors are determined. Dependences of the coefficient of computational efficiency and the coefficient of increase in the registers of the three-stage interpolated low-pass filter on the values of the interpolation factors, the widths of the passband and the transition band are obtained. Relations for determining the optimal values of interpolation factors corresponding to the maximal value of computational efficiency coefficient are obtained. In addition, the dependencies of the maximum coefficient of computational efficiency and the optimal coefficient of increase in the registers of the three-stage interpolated low-pass filter on the widths of the passband and the transition band at the optimum values of the interpolation factors are obtained. Considered three-stage interpolated low-pass filters should be used in the case when the required stopband is significantly less than the sampling rate. In this case, three- stage interpolated filters require less computational resources for calculating the response than the two-stage interpolated filters or filter implemented by the transversal structure.