To provide a method and a program for obtaining a transfer function of a high order of an FIR filter having a minimum phase transition characteristic by using a sequential projection process.

In this filter design method by directly approximating a transfer function of the FIR filter having the minimum phase transition characteristic by using the sequential projection process, the restriction of a predetermined condition is given to a step size necessary in updating the n-th coefficient of the sequential projection process, and a root of the transfer function is limited on a unit circle or in a unit circle. Whereby the factorization becomes unnecessary, the design of the transfer function of a higher order in comparison with a conventional one, is available, a memory necessary for calculation can be reduced, and the algorithm is composed of simple repeats.