# 13 Spectral Estimation Methods for Signal Analysis

Here is the True PSD for a given Test data

The following are PSD Estimations from SpectrumSolvers (tm) for given Test data

 Burg LSMYWE Periodogram

Which of above Estimations is best?
Which of above Estimations is worst?

SpectrumSolvers (tm) program calculates a Power Spectral Density (PSD) estimate from 1 of several Steve Kay's Estimators. Try all methods and compare them. Which is best on your data? Kay's modern Estimators have shed new light on signal detection. Detecting a signal 50+ dB down is now -very- possible.

SpectrumSolvers (tm) has a menu of Spectral estimators from Steve Kay's textbook, titled "Modern Spectral Estimation", 1988. The results differ dramatically from one estimator to another. Plus, varying input parameter(s) and/or number of points may show discrepancies.

Estimation methods in SpectrumSolvers include Autocorrelation, Covariance, Prony, Akaike, Burg, Recursive Maximum Likelihood Estimation, Modified Yule-Walker Equations and others.

This picture/plot shows a PSD plot for one of the thirteen methods available to choose from. The methods can vary dramatically in their results. Try several before choosing which estimation is best to represent your PSD.

Manufacturing companies take note! Some estimators can detect signals 50 to 100 dB from main signal. See documented example! The unwritten rule of '30 dB is okay' (i.e. hidden) is no longer true.

See how zero padding effects ones results. Ability to change array sizes on the fly and thus show zero padding effect is/was main reason for writing this software. SpectrumSolvers is a free (3 MB) download.

Note: Fortran and Visual Basic source files are included.

## Key factors behind Spectral Estimator Methods _____________Fourier Transform (FT) vs.Transfer Function Approach

Given Δt & no. of data points (npoints) determines Δf by the relation:
 Δf = 1 Δt * (npoints - 1)

The smaller 'Δt' the larger 'Δf. Thus, many data points are often required in order to reduce 'Δf' to a desired size. This relationship shows the problem one will have when trying to use the integration operator for a solution

Others got the idea that a transfer function H(s) with poles & zeroes may provide better properties for a Spectral Estimator algorithm than the common Fourier Transform.

Here Δf is independent of npoints.  A few data points will provide a pole or two and thus start you on your way. Add some zero-padding to improve your plot resolution.

This approach detects key frequencies much better than the FT does. Data windowing is NOT an issue.

### SpectrumSolvers 6.21 Output Plots:

(Click Any Image To Enlarge)

Power Spectral Density (PSD) Plot

## PSD 3D Plot

A 3D plot of ones spectrum as time goes on is achieved by calculating new PSD plots every delta_print time; i.e. every 'second' or two calculate another PSD plot. Then stand them up side by side so you get a plot like the one below.

### (x = Frequency, y = Time, z = PSD Amplitude in dB) ------------------------------------

Last Updated: Oct. 28, 2019
First Published: 1994
Requirements:Windows + Visual Basic 6.0 RunTime files
Publisher: Optimal Designs Enterprise

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