Abstract: Fractional delay compensation is very important in digital signal processing. In this paper, several compensation methods are discussed, including the least-squares filtering, Lagrange interpolation, and filter groups based on the Farrow structure. We conclude after simulations that the Lagrange interpolation method has the advantage of concision, easy implementation, and wide adaptability. On the otherhand, the Farrow structure is a powerful way to control delay variation. It is more effective to combine the Farrow structure with the Lagrange interpolation. We present the details of the design of filter groups of the Farrow structure based on the Lagrange interpolation. We implement the combined method for processing the telemetry signals from the Mars Express mission and compare the results to those of the traditional frequency-domain compensation method.