A signal processing apparatus includes: a coefficient update unit configured to approximate a characteristic of a transmission line of an optical signal by a first tap coefficient vector of which an L0 norm is a predetermined value or less; a zeroing unit configured to generate a second tap coefficient vector by replacing, with 0, a tap coefficient of which an absolute value is less than a threshold among tap coefficients of the first tap coefficient vector; and an adaptive filter configured to perform, based on the second tap coefficient vector, adaptive equalization processing on a digital signal corresponding to an optical signal received via the transmission line.