A novel ROM compression architecture for DDFS utilizing the parabolic approximation of equi-section division

In this paper, we propose the parabolic approximation of equi-section division (PAESD) utilizing the symmetry property and amplitude approximation of a sinusoidal waveform to design a direct digital frequency synthesizer (DDFS). The sinusoidal phase of a one-quarter period is divided into equi-sections. The proposed method utilizes the curvature equivalence to derive each parabolic curve function, and then the value of the error function between each parabolic curve function and the sinusoidal function is stored in an error-compensation ROM to reconstruct the real sinusoidal waveform. The upper/lower bound of the maximum error value stored in the error-compensation ROM is derived to determine the minimum required memory word length relative to the number of bits of the equi-sections. Thus, the minimum size of the total ROMs of the DDFS using the PAESD without error-compensation ROM is compressed to 544 bits; the total compression ratio, compared with the minimum size of the total ROMs of the DDFS using the basic look-up table (LUT), is approximately 843:1, achieved by consuming additional circuits [71 adaptive look-up tables (ALUTs), 3 digital signal processor (DSP) block 9-bit elements]. Consequently, the results show that the proposed ROM compression method can effectively achieve a better compression ratio than the state-of-the-art solutions without affecting the spectrum performance of an average spurious-free dynamic range (SFDR) of -85 dBc.