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Digital direct frequency synthesizer (DDFS) can be used to correct the carrier frequency offset (CFO) whose estimation and recovery are essential important in OFDM receiver systems. Traditional DDFS makes use of modulus 2N arithmetic and may provide fine frequency tuning capabilities using a sine/cosine look up table. However, straightforward implementation results in enormous amounts of memory and power consumption. This paper proposes a novel DDFS according to the adopted CFO recovery scheme, in which the integer CFO is corrected after the FFT by summing a constant to the index used to read the results of the FFT and the decimal CFO can be compensated with tuning on the increment word of the DDFS of the mixer. Its phase accumulator and ROM are split into three smaller parts based on the trigonometric approximate. Further, according to their characteristics each one has been compressed. Performance analysis has been carried out and shows that 96% and 61% memory reduction can be achieved compared with Moran and Memoyo's method and Kesoulis's method, respectively. The design will be implemented in OFDM such as DVB-T systems.