On Fast and High Precision RMS Value Estimate of Frequency Varying Sinusoids

Abstract

A precision RMS value estimation (0.05%~0.3% accuracy) algorithm feasible for DSP chip implementation in real-time processing of periodic waveform is proposed. This has application in digital power meter design. In here measurement of a sinusoid in white noise environment (SNR=17 dB) with frequency range from 20 Hz to 500 Hz varied at the rate from 1 cycle to 3 cycles is considered. To achieve the required accuracy direct computation of [T^(-1)•∫(superscript to+t1 subscript t0) x^2(t)dt](superscript 1/2) is used which is then approximated by the discrete version of the formula that adopts dense sampled data (48 kHz) together with an accurate (0.1%) period (or frequency) estimate. Due to finite data size is used the windowing effect (frequency window sidelobe) causes the maximum point of the Periodogram (estimated frequency) much off the true frequency. Our proposed method uses a novel recursive Window Adjustment Periodogram for the frequency estimate. With proper windowing as the length in time domain is stretching or shrinking the nulls of frequency window sidelobes gradually approach and finally coincide with the spectral line other than the frequency of interest. Simulation results show this algorithm converges to the desired period estimate within few loops.