The ringing occurred in the step response causes an undesirable stripe pattern in TV signals. A simultaneous approximation with both the frequency and the step response is required in the designing filter which is used in the image signal processing in order to prevent the ringing. The wellknown Remez algorithm for designing FIR filters approximates the response only in the frequency domain. As the result, the filters designed by this algorithm causes the large ringing in the step response. In this paper, we propose the method of design for FIR filters with minimum amplitude in the stopband, under the condition that the step response has no ringing and the prescribed rise characteristics. For this end, we use the constrained successive projections method.

The transfer function of IIR all-pass filters is a rational function of ω. However, the optimization of such a rational function using the successive projections method, which has a wider range of application than the Remez algorithm, has not been presented. In this paper, we propose designing IIR all-pass filters using the successive projections method.