A filter generation apparatus includes: a coefficient calculation unit that performs IFFT on a frequency characteristic of a frequency domain filter and calculates a filter coefficient of a linear phase FIR filter; a conversion unit that converts the filter coefficient to a filter coefficient of a minimum phase FIR filter; a coefficient generation unit that generates a filter coefficient of an approximation filter by executing cut-out processing to a filter length set by a filter length setting unit and rounding processing performed by a window function on the filter coefficient; an error calculation unit that calculates an error of a frequency characteristic corresponding to the approximation filter with respect to the frequency characteristic of the frequency domain filter; and a filter storage unit that stores the filter coefficient therein as a filter coefficient that specifies a new filter when the error is equal to or less than a predetermined threshold value.