Influence of Additive White Gaussian Noise on the Interpolation Method of Discrete Spectrum

Abstract:

Without noise, the interpolation method of discrete spectrum is accurate except rounding error. However, the estimation accuracy is declined when a signal corrupted with noise, and even turns out to be meaningless. The paper investigates the influence of additive White Gaussian Noise on the accuracy of amplitude and phase based on interpolation method. Analytical expressions of the estimator variance for amplitude and phase correction are derived. Simulation results confirm the validity of the presented analysis.

• Periodical: Advanced Materials Research (Volumes 383-390)
• Pages: 2951-2957
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.383-390.2951
• Online since: November 2011
• Authors: Chuan Yan Xu, Kang Ding, Zhi Jian Yang, Hui Bin Lin
• Keywords: Interpolation Method, White Gaussian Noise, Window Function

References

[1] Thomas Grandke. Interpolation algorithms for discrete fourier transforms of weighted signals[J]. IEEE Transactions on Instrumentation and Measurement. 1983, 32(2): 350~355.

DOI: 10.1109/tim.1983.4315077

[2] DAVID C. RIFE and R.R. BOORSTYN 1974 IEEE Transactions on Information Theory 33, 591-598. Single-tone parameter eatimation from discrete-time observations.

DOI: 10.1109/tit.1974.1055282

[3] Schoukens J, Rik Pintelon, Hugo Van Hamme. The interplotated fast transform: a comparative study[J]. IEEE. Trans. Instrum. 1983, 32(2): 350-355.

DOI: 10.1109/19.137352

[4] Carlo Offelli and Dario Petri. The influence of windowing on the accuracy of multifrequency signal parameter estimation[J]. IEEE Transactions on Instrumentation and Measurement. 1992, 41(2): 256-261.

DOI: 10.1109/19.137357

[5] D. C. Rife and R. R. Boorstyn. Single-tone parameter estimation from discrete-time observations[J]. IEEE Trans. Inform. Theory, 1974, IT-20: 591-598.

DOI: 10.1109/tit.1974.1055282

[6] S Umesh and D. Nelson. Computationally efficient estimation of sinusoidal frequency at low SNR. Proceedings of the IEEE Conference on Acoustics, Speech and Signal Processing[J]. 1996, Atlanta: 2797-2800.

DOI: 10.1109/icassp.1996.550134

[7] Yang Zhijian, Ding Kang. Theoretical Research on Discrete Spectrum Correction and Application in Vibration Anaylsis of an Engine[D]. Doctoral Dissertation. 2009. 4.

[8] Xie Ming, Ding Kang, Correction for the frequency, amplitude and phase in FFT of harmonic signal[J]. Mechanical System and Signal Processing. 1996, 10(2): 211-221.

DOI: 10.1006/mssp.1996.0015

[9] Ding Kang, Xie Ming, Yang Zhijian, The Theory and Technology of Discrete Spectrum Correction. Beijng: Science Press, 2008, pp.170-192.