A signal processing apparatus includes a phase shift unit and a signal processing unit. The phase shift unit shifts phases of at least one set of first periodic signals and second periodic signals. The first periodic signals are output from an optical signal output device connected to a displacement detection target and have amplitude gradually increasing with a displacement in a predetermined direction of the displacement detection target. The second periodic signals are output from the optical signal output device connected to the displacement detection target and have amplitude gradually decreasing with the displacement in the predetermined direction of the displacement detection target. The signal processing unit executes a predetermined operation with respect to the first and second periodic signals output from the phase shift unit to obtain a displacement of the displacement detection target.