1. NONPARAMETRIC METHODs (NPM) OF POWER SPECTRAL DENSITY ESTIMATION P. by: Milkessa Negeri (…M.Tech) Jawaharlal Nehru Technological University,India December 04,2017

2. Definitions Of terms:  The power spectral density (PSD) of the signal: Is the power present in the signal as a function of frequency/per unit frequency. (Unit=W/Hz or Db/Hz)  A Signal is decomposed into a number of spectrum of frequencies over a continuous range.  Spectrum:- Is representation of a signal by summation of its various sinusoids with different Frequencies & Amplitudes.  So, PSD is distribution of power into frequency components composing that signal.

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4. There are 2 methods of estimating PSD [1] Parametric methods: Find the parameters for a mathematical model describing a signal, system, or process.  These techniques use known information about the system to determine the model. [2]Nonparametric:-We are going to see this in detail. Estimation: Estimation Is approximating O/put of a system after it’s degraded by noise or distortion. So, for random signals, only an estimate can be obtained. 4

5. GENERAL PROPERTIES OF NPMs  NPMs: do not make any assumptions on the data-generating process or model  Rely on the direct use of the given finite duration signal to compute the Autocorrelation,  to the maximum allowable length (beyond which it is assumed zero),  Rely on FT and FFT.  FFT: Is an algorithm that samples a signal over a period of time (or space) and divides it into its freq. components having d/t amplitude. 5

6. There are 5 Nonparametric PSE methods: [i] Periodogram Method [ii] Modified Periodogram method [iii] Bartlett’s Method [iv] Welch’s Method [v] Blackman-Tuckey Method  The methods are evaluated & compared by 4 Xcs:  Spectral resolution,  Asymptotic bias,  Variance and  Complexity. 6

7. Explanation of characteristics 7

8. 1.PERIODOGRAM  the estimates are based entirely on a finite record of data x(n) w/c is generally a problem of all NPMs. So, Periodogram is, 8

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16. Properties of Periodogram 16

17. Drawback comments on Periodogram: 17

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20. 2. MODIFIED PERIODOGRAM 20

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22. 3.BARTLETT METHOD 22

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24. 4.BLACKMAN TUCKY METHOD 24

25. 5.WELCH’S METHOD 25

26. PERFORMANCE COMPARISON 26

27. QUALITY FACTOR 27

28. Computational requirements 28

29.  2 N additional computation is required for windowing.  For Blackman-Tukey power spectral estimate  We cant use N point DFT for its computation because its maximum value limits to 1024 point DFT,  for which we require 2M point DFT and one 2M point IDFT  Hence we are using the FFT algorithm as follows 29

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31. example Ex. A frequency resolution is 0.09 and N=100 samples. Determine the quality factor, recorded length and no. of computation requirements for Bartlett, Welch and Blackman – Tukey methods. Givens; frequency resolution: Δf = 0.09 Samples: N=100 Required: QF,M and No. of computation requirements for B,W & BT methods. Solutions: 31

32. Solutions 32

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35. CONCLUSION 35

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37. References [1] Statistical and Adaptive Signal Processing, D. Manolakis, V. Ingle, S. Kogon, 2005, Artech House. [2] Statistical Digital Signal Processing and Modeling, M. M. Hayes, 1996, Wiley. [3] Modern spectral estimation, S. M. Kay, 1988, Prentice Hall. [4] D.J. Thomson, “Spectrum estimation and harmonic analysis,” Proc. IEEE, vol. 70, no. 9, pp. 1055–1096, 1982. [5] www.mathworks.comwww.mathworks.com [6] Statistical Digital Signal Processing And Modelling,Monson H. Hayes 37