To provide an FIR filter which can prevent break of equal ripple of weighted approximation error and maintain the gain in a pass band to be an almost constant value, and a method for setting coefficients of the filter.

This method for setting filter coefficients of the FIR filter has an initial setting step (F101) for setting the FIR filter, setting a band, setting coefficients of a pre-filter, and setting an initial extreme value point, a first step (F102) for producing an interpolation polynominal which interpolates amplitude characteristic from the extreme value point of amplitude characteristic of frequency, a second step (F103) for determining a new extreme value point from amplitude characteristic obtained from the interpolation polynominal obtained in the first step, a third step (F104) for repeating the first and second steps and judging whether the position of the extreme value point is made approximate in a desired range, and a fourth step (F105) for obtaining the filter coefficients from the amplitude characteristic which is approximated in the third step.