The application discloses a tuner and a method for tuning a signal. The tuner comprises: a sampling module, the sampling module being configured to receive an input signal and a set of control signals, sample the input signal under the control of the set of control signals and generate a sample signal; wherein each of the set of control signals has a control period equal to (N*TVCO), and the control periods of the set of control signals synchronize with each other; a set of weighting modules, wherein each of the set of weighting modules is configured to receive the set of sample signals and weight the received sample signals with a group of weighting factors to generate a group of weighted signals; and one or more summing modules, each summing module being configured to receive one group of weighted signals generated by one of the set of weighting modules and sum the group of weighted signals to output an output signal, wherein the output signal is the input signal being shifted by a predefined frequency fVCO*mk/N.