A method for interpolating an encoded signal of encoders is disclosed. The first step may include generating four first stage signals having a first frequency that are 45 degrees out of phase. The four signals may then be multiplied to obtain a plurality of second stage signals that are 90 degrees out of phase having a second frequency two times the first frequency. The second stage signals may then go through further computation to obtain a plurality of third stage signals that are 45 degrees out of phase. The third stage signals may be further adapted for further multiplication to obtain higher levels of interpolation. Interpolators and optical encoders characterized by the interpolation capability are also disclosed.