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

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Title:	On Fast and High Precision RMS Value Estimate of Frequency Varying Sinusoids 高精密度數位功率分析儀的演算法研究
Authors:	劉宗慶
Contributors:	華岡工程學報
Date:	1995-07
Issue Date:	2014-11-04 15:57:23 (UTC+8)
Abstract:	最新高性能功率分析儀已朝Digital Signal Processing (DSP)的方向發展（美Xitron、日Yokogawa使用16bit A/D、32-bit DSP Chip），頻率的估計準確度爲0.05%~0.1%，範圍爲0.001Hz~500KHz，測試速度爲0.01s~250ms，均方值(RMS value)的準確度在0.05%~3%。國內欲發展同級數之功率分析儀，在避免觸及專利的前提下，必須克服此高速、高精確的頻率估計之方法。本研究在發展以全新的Recursive Periodogram方法達成高速高精確的頻率估計，進而得到高精確之均方值估計。 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.
Relation:	華岡工程學報； 9 期 (1995 / 07 / 01) ， P205 - 214
Appears in Collections:	[College of Engineering] Chinese Culture University Hwa Kang Journal of Engineering

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