Systems and methods for generating gapped signals comprising a Delta Sigma Modulator (DSM) configured to generate gapping control signals used to control gap removal rates of an associated gapping unit. The DSM is configured to generate a gapping control signal based on a value of an overflow resulted from performing adding a first number with a remainder of a stored value modulo a second number. The gap removal rates as well as the gap removal resolutions can be adjusted by selecting appropriate values of the first number, the stored value, and the second number. The gapping resolution can be a portion of a pulse. The first number and the second number may be derived from an intended frequency ratio between a gapped signal and a corresponding input signal. The gapping unit may comprise a gapping circuit or a multi-modulus divider.