Method of computing fir filter coefficient and program for computing same

A program for computing FIR filter coefficients, the program causing a computer to execute the steps of:

• determining every element of a single-dimension array B′ using a filter order N being a positive integer of a universal maximally flat FIR filter, a number of zeros K at z=−1, K being an integer equal to or more than zero, and a parameter d for a group delay at z=1, d being a rational number, all of which are provided by inputs, by changing in sequence an index j from 1 to N−K in a recurrence formula B′[j]=(−1)×{(2d)B′[j−1]+(j−1)B′[j−2]}/(N−j+1), the single-dimension array having N+1 elements B′[j] where 0≦j≦N, in which an element B′[0] thereof is initialized to 1 and all the elements thereof except the element B′[0] are initialized to zero;
• determining every element of a three-dimension array r by sequentially changing, in the order of indexes j, i, p, an index j from 0 to N-p, and an index i from 0 to p, an index p from 1 to N in a recurrence formula r[p,i,j]=(r[p−1,i−1,j]−r[p−1,i−1,j+1])/2+(r[p−1,i,j]+r[p−1,i,j+1])/2, the three-dimension array r having N3 elements r[p,i,j] where 0≦p≦N, 0≦i≦N, 0≦j≦N, in which elements r[0,0,j] thereof where 0≦j≦N−K are initialized to elements of the single-dimension array B′[j] where 0≦j≦N−K, and all the elements thereof except the elements r[0,0,j] are initialized to zero;
• and
• extracting elements r[N,i,0] of the three-dimension array r where 0≦i≦N as the impulse response coefficients of the universal maximally flat FIR filter.