A signal processing apparatus includes a first filter on an in-phase signal channel; a second filter on a quadrature signal channel; a plurality of filter stages having each of more than one signal paths crossing each other which connects the first filter and the second filter; and at least more than one of the filter stages of more than one of a plurality of the filter stages includes a switching circuit disconnecting more than one of the signal paths and a correction unit correcting direct current offsets of the first filter and the second filter by using the switching circuit.