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PSD computations using Welch's method. [Power Spectral Density (PSD)]
Open accessAbstract
This report describes Welch's method for computing Power Spectral Densities (PSDs). We first describe the bandpass filter method which uses filtering, squaring, and averaging operations to estimate a PSD. Second, we delineate the relationship of Welch's method to the bandpass filter method. Third, the frequency domain signal-to-noise ratio for a sine wave in white noise is derived. This derivation includes the computation of the noise floor due to quantization noise. The signal-to-noise ratio and noise flood depend on the FFT length and window. Fourth, the variance the Welch's PSD is discussed via chi-square random variables and degrees of freedom. This report contains many examples, figures and tables to illustrate the concepts. 26 refs.
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“The hamming window is applied during the FFT to filter out the noise and unwanted signal from captured data, which affects the ENBW and, consequently, the PSD calculation [55].”
From Multiwavelength Photoacoustic Doppler Flowmetry of Living Microalgae Cells (2024) · cites this paper as [55]
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Cited by 72
Research works printed but not linked: 15
- J. S. Bendat and A. G. Piersol, Random Data: Analysis and Measurement Procedures, New York: John Wiley & Sons, Inc., 1986.
- J. W. Cooley and J. W. Tukey, "An Algorithm for Machine Computation of Complex Fourier Series," Mathematics o f Computation, Vol. 19, April 1965, pp. 297-301.
- Svend Gade and Henrik Herlufsen, "Windows to FFT Analysis," Sound and Vibration, March 1988, pp. 14-22
- Svend Gade and Henrik Herlufsen, "Windows to FFT Analysis (Part 1)," Bruel & Kjaer Technical Review, No. 3, 1987, pp. 1-28.
- Svend Gade and Henrik Herlufsen, "Windows to FFT Analysis (Part 11)," Bruel & Kjaer Technical Review, No. 3, 1987, pp. 1-35.
- F. J. Harris, "On the Use of Windows for Harmonic Analysis with the Discrete Fourier Transform," Proceedings o f the IEEE, Vol. 66, No. 1, January 1978, pp. 51-83.
- IEEE Trial-Use Standard fo r Digitizing Waveform Recorders, IEEE Std 1057, IEEE, New York, NY, July 1989.
- L. H. Koopmans, The Spectral Analysis o f Time Series, New York: Academic Press, 1974.
- A. H. Nuttall, "Some Windows with Very Good Sidelobe Behavior," IEEE Transactions on Acoustics, Speech and Signal Processing, Vol. ASSP-29, No. 1, February 1981, pp. 84-91.
- A. Papoulis, Probability, Random Variables and Stochastic Processes, New York: McGraw-Hill Book Company, 1965.
- W. H. Press, B. P. Flannery, S. A. Teukolsky and W. T. Vetterling, Numerical Recipes in C, New York: Cambridge University Press, 1988.
- M. B. Priestley, Spectral Analysis and Time Series, Volume 1, New York: Academic Press, 1981.
- J. Schoukens and J. Renneboog, "Modeling the Noise Influence on the Fourier Coefficients After a Discrete Fourier Transform," IEEE Transactions on Instrumentation and Measurement, Vol. IM-33, No. 3, September, 1986.
- P. D. Welch, "A Direct Digital Method of Power Spectrum Estimation," IBM Journal, April, 1961.
- P. D. Welch, "The Use of Fast Fourier Transform for the Estimation of Power Spectra: A Method Based on Time Averaging Over Short, Modified Periodograms," IEEE Transactions on Audio and Electroacoustics, Vol. AU- 15, No. 2, June, 1967. Distribution: Charlie Adams Dave Martinez John Red-Horse Bill Millard Ed Clark 2334 Stu Kohler Bill Hensley Ruth David Wayne Lathrop Bob Peet 2715-2 Carl Dreyer Jeanne Bando Jerry Biedscheid Bob Isidoro M ike Rogers Otis Solomon (20) Doug Dederman Don Thalhammer Jim Nakos Tom Baca Jerry Cap Bill Dunn Bill Sieger Ervin Smith John Snethen Roger Zimmerman Ron Rodeman Vesta Bateman Tom Came 2743 Neil Davie 2743 Jim Lauffer 2743 Randy Mayes 2743
Metadata
- Authors
- Solomon, Jr.
- Corresponding author
- Solomon, Jr, O M
- Published
- 1991-12-01
- OpenAlex
- W2236853541
- Cited by
- 72
- References
- 0
- Citations by year
- 2026: 9 · 2025: 16 · 2024: 8 · 2023: 10 · 2022: 9 · 2021: 8 · 2020: 7 · 2019: 4 · 2015: 1
- Type
- report
- Language
- en
- Open access
- green
- www.osti.gov
- Locations
- OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) (submittedVersion)
- Topics
- Physical Sciences › Computer Science › Signal Processing › Digital Filter Design and Implementation
- Physical Sciences › Engineering › Electrical and Electronic Engineering › Advanced Electrical Measurement Techniques
- Physical Sciences › Mathematics › Applied Mathematics › Statistical and numerical algorithms
- Keywords
- power spectral density, Welch's method, spectral estimation, quantization noise, noise floor, chi-square distribution, white noise
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