Spectral Estimation Methods SpectrumSolvers 6.12 ... a dozen methods that beat the FFT!



13 Spectral Estimation Methods
for
Signal Analysis

'AutoCorr' w/10 poles; 50dB of Signal's Spectrum

Here is the True PSD for a given Test data

True PSD for given Test data

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

Burg PSD Estimation
Burg

LSMYWE PSD Estimation
LSMYWE

Periodogram PSD Estimation
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.

Picture of a generalized Transfer Function

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 6.12 Output Plots:



(Click Any Image To Enlarge)

Power Spectral Density (PSD) Plot
Power Spectral Density 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.

Spectral 3D Plot

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

SpectrumSolvers 6.12
Download (3MB) Information:



Last Updated: June 23, 2017
First Published: 1994
License: Freeware Free
OS: Windows XP or newer
Requirements:Windows + Visual Basic 6.0 RunTime files
Publisher: Optimal Designs Enterprise

SpectrumSolvers 6.12
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 4.  SpectrumSolvers: Spectral Estimation Methods; and compare them.
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Problem-Solving Applications include:

CurvFit: a curve fitting program with Lorentzian, Sine, Exponential and Power series are available models to match your data.

Match-n-Freq: a Matched Filter program used to filter signals and slim pulses.

Industry Problem-Solving Descriptions include:

Electrical Filter Design: find the transfer function's poles & zeros; H(s) = Yout(s) / Yin(s).

Pulse Slimming to minimize InterSymbol Interference: via Arbitrary Equalization with Simple LC Structures to reduce errors.

Voice Coil Motor: basically an electromagnetic transducer in which a coil placed in a magnetic pole gap experiences a force proportional to the current passing through the coil.

AC Motor Design: a simulation program for A.C. motor design that was reapplied as a constrained optimization problem with 12 unknown parameters and 7 constraints.

Digitized Signal from Magnetic Recording: Magnetic recording of transitions written onto a computer disc drive may produce an isolated pulse as shown.

PharmacoKinetics: an open-two- compartment model with first order absorption into elimination from central compartment is presented here.


 
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Increasing Productivity Examples: AC Motor Design - Matched Filters - Pulse Slimming / InterSymbol Interference - Pilot (safe) Ejection - PharmacoKinetics Simulation - Poisson's (Differential) Equation - Schrodinger (Differential) Equation - BVP 4 PDE Equations - Implicit (Differential) Equations