Design of two‐stage cascade FIR digital filters with coefficients of limited word‐length
Satoshi Imai, Yutaka Fukuda · Electronics and Communications in Japan (Part I Communications) · 1988
Abstract It is shown that the two‐stage cascade construction is very effective in the realization of a digital filter with a sufficiently large attenuation in the stop‐band. A design method for the two‐stage cascade FIR filter with limited word‐length is described. Compared with the direct construction, the word‐length of the filter coefficient in the two‐stage cascade FIR filter is reduced to less than 60 percent. In general, compared with the direct construction, the word‐length of the filter coefficient is reduced in the cascade construction, while the order is increased. However, in the proposed method, the order of the two‐stage cascade construction need not be very large, compared with the case of direct construction, being 1.5 times in the worst case. By imposing less strict limitation on the word‐length of the filter coefficient, the order of the two‐stage cascade construction FIR filter never exceeds 4/3 times that of the direct‐type FIR filter. In the realization of a linear‐phase, two‐stage cascade FIR filter, lower‐order minimum‐ and maximum‐phase filters than the linear‐phase filter can be applied as subfilters. This is effective in further reducing the order of the two‐stage cascade FIR filter, thereby reducing the order to 0.8 to 0.9 times the case of the construction based on the linear‐phase subfilter.