Phase locking scheme based on look-up-table-assisted sliding discrete fourier transform for low-frequency power and acoustic signals

The frequency tracking performance of sliding discrete Fourier transform (SDFT)-based phase locking (PLL) scheme has been improved by supplementing a cosine look-up table (cLUT) loop. Since the SDFT algorithm is marginally stable, to avoid instability, a damping factor is introduced, which causes the steady-state error in the PLL behaviour. The addition of cLUT indirectly strengthens cosine component of SDFT output and eliminates the effect of damping factor. Consequently, the numerically controlled oscillator (NCO) yields accurate sampling frequency, and it could be utilised to generate unit sine and cosine reference signals, synchronous with the periodic input signal in power system applications. A mathematical model of the look-up table (LUT) assisted SDFT-based PLL has been developed to analyse the transient and steady-state behaviour and it substantiates the improvement in steady-state performance. The PLL exhibits second order under damped response resulting in faster acquisition and small reduction in pull-in range with zero steady-state error. The improvement in performance of the LUT-assisted SDFT PLL is investigated by simulation and experimental studies.