A device is disclosed that includes a control module and a gain estimation module. The control module is configured to superimpose two non-zero values on a frequency control word to respectively generate a first and a second modified fractional reference phase signals, under a condition that a fractional part of the frequency control word is smaller than a predetermined value. The gain estimation module is configured to calculate a first and a second estimated gain values respectively based on the first and the second modified fractional reference phase signals. The control module is further configured to calculate an estimated digital-to-time converter gain value based on an interpolation of the first and the second estimated gain values.