A signal processing apparatus includes: a filter; and a filter control circuit, wherein the filter control circuit is configured to: detect a power of signals output from the filter; determine one of a plurality of numerical ranges to which the power belongs; update a filter coefficient of the filter according to a determination result; count a number of the signals having the power of a first value or more; set an invalid area which becomes a target not to be determined for each of one or more boundaries between the plurality of numerical ranges when the number of the signals becomes a second value or more; and control a width of the invalid area based on the number of signals.