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Rainbow 5.11.5 ... a dozen methods that beat the FFT!
13 Spectral Estimation Methods
for
Signal Analysis
- Here is the True PSD
for a given Test data
The following are PSD Estimations from Rainbow (tm) for given Test
data
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Burg
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LSMYWE
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Periodogram
Which of above Estimations is best?
Which of above Estimations is worst?
- Rainbow (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.
- Rainbow (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 Rainbow 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. Rainbow
is a free (1.3 MB) download.
Key factors behind
Spectral Estimator Methods
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Fourier Transform (FT)
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vs.
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Transfer Function Approach
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Given Δt & no. of
data points (npoints) determines Δf by the relation:
| Δf = |
1
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| 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
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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.
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Rainbow 5.11.5 Output Plots:
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(Click Any Image
To Enlarge)
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Power
Spectral Density (PSD) Plot
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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)
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Rainbow 5.11.5
Download (1.3MB) Information:
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- Last Updated: Sept. 24, 2008
- License: Freeware Free
- OS: Windows Vista, 2003, XP, 2000, 98,
Me, NT, CE
- Requirements: Some parts require Win
95/98
- Publisher: Optimal Designs Enterprise
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Rainbow 5.11.5
Click on right Link to
Download Now
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Description (Click to download)
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Price
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4.
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Rainbow:
Spectral Estimation Methods; and compare them.
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$0.00
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HTML code
for linking to this page:
- <a
href="http://www.digitalCalculus.com/demo/rainbow.html"><img
align="middle" width="100"
src="http://www.digitalCalculus.com/image/rainbow-icon.gif"/>
<strong>Compare 13 Spectral Estimation Algorithms</strong>
</a>, Spectral Estimation Methods, Signal Analysis, Signal
Processing.
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