One of the advantages of direct frequency synthesis technique (e.g., flying-adder architecture) is its capability of generating arbitrary frequency by utilizing the time-average-frequency concept. In the clock output of the direct frequency synthesizer, instead of one type of cycle, there are two types of cycles. Unlike the conventional one-type-cycle clock wherein clock energy is concentrated at its designed frequency, Time-Average-Frequency based clock spreads some of its energy into spurious tones, which could be harmful to certain applications. The spurious tones are caused by the periodic carry sequence generated from a fractional part accumulator inside the frequency synthesizer. The invention suggests a method and an apparatus to break this periodicity and convert the spurious tones into broadband noise.