In this paper, we present a numerical method for the equiripple approximation of IIR digital filters. The conventional rational Remez algorithm quickly finds the squared magnitude response of the optimal IIR digital filters, and then by factorizing it the equiripple filter is obtained. Unlike the original Remez algorithm for FIR filters, it is difficult for the rational Remez algorithm to explicitly control the ratio of ripples between different bands. In the conventional lowpass filter design, for example, when different weights are given for its passband and stopband, one needs to iteratively design the filter by manually changing the weights in order to achieve the ratio of the weights exactly. To address this problem, we modify the conventional algorithm and make it possible to directly control the ripple ratio. The method iteratively solves eigenvalue problems with controlling the ripple ratio. Using this method, the equiripple solutions with desired weights are obtained automatically.

In this paper, we present a numerical method for the equiripple approximation of minimum phase FIR digital filters. Many methods have been proposed for the design of such filters. Many of them first design a linear phase filter whose length is twice as long, and then factorize the filter to obtain the minimum phase. Although these methods theoretically guarantee its optimality, it is difficult to control the ratio of ripples between different bands. In the conventional lowpass filter design, for example, when different weights are given for its passband and stopband, one needs to iteratively design the filter by trial and error to achieve the ratio of the weights exactly. To address this problem, we modifies well-known Parks-McClellan algorithm and make it possible to directly control the ripple ratios. The method iteratively solves a set of linear equations with controlling the ratio of ripples. Using this method, the equiripple solutions are obtained quickly.

For the multi-gray shades image in the passive matrix type STN-LCDs, the method which combined space modulated patterns and frame rate control(FRC)with switched some frames has been used. Although bi-level display elements are used this method makes it possible to display a multi-gray shades image without resolution-loss for still-image, while the method has a fault to perceive interference of flicker at low frame rate, as is wellknown. However the measured quantitative data for flicker and frame frequency have hardly be published. With regard to frame rate control method which some typical space modulated patterns are combined, we measure critical flicker frame frequency(CFFF) with subjective experiments. This paper also discribes that the data are arranged to be shown in form of relationship with the screen luminance and the lowest frequency components included among ripples on times and also the ripples ratio. Our experimental study provides useful data for designing such kinds of display.