In many position sensing applications, position detection of the target sensing element is typically based on the two-phase orthogonal displacement signals, i.e., sine and cosine, that are directly sensed from the sensors. In this letter, an approach of sensing multiphase sinusoidal signals from the multiple sensors is considered, and a mathematical method of transforming the multiphase sinusoidal signals into the two-phase orthogonal signals is presented. A system of linear equations is established based on the relationship that each of the sensed multiphase sinusoidal signals can be represented by components of two-phase orthogonal signals. By solving the system of linear equations, two-phase orthogonal signals are obtained from the multiphase sinusoidal signals. The resulting transformation of the multiphase sinusoidal signals into the two-phase signals is lossless and overcomes the distortions in sensed signals substantially. The techniques of multiphase signal processing are shown to greatly improve the position accuracy by computer simulation and prototyping of Hall sensor encoders.