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The
Chromatic Derivatives and the Chromatic Approximations
Home Page What are the chromatic derivatives? You can read the
extended abstract or introduction of this paper This page is intended
to be a convenient “one stop” repository of papers, preprints, technical
reports, patents, etc. on chromatic derivatives and chromatic expansions,
especially for items that are hard to find elsewhere. The material is posted
with permission from the authors. Disclaimer: These documents are made available to ensure timely dissemination of
scholarly work. Copyright and all rights therein are retained by the copyright
holders. All parties copying this information are expected to adhere to the
terms and constraints invoked by each copyright holder. In most cases, these
documents may not be reposted without the explicit permission of the
copyright holder. Other restrictions to copying individual documents may
apply. |
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KROMOS TECHNICAL REPORTS, 2001 |
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1. Aleksandar Ignjatovic: Numerical Differentiation and Signal Processing, Kromos
Technical Report 1, 2001. |
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2. Timothy Herron and John Byrnes: Families of Orthogonal Differential Operators for Signal
Processing, Kromos Technical Report 2, 2001. |
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3. Aleksandar Ignjatovic: Introduction
to Signal Processing Based on Orthogonal Differential Operators, Kromos Technical Report 3, 2001. (an abbreviated version
of 1 above) |
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4. Mathew Cushman and Timothy Herron: The General Theory of Chromatic Derivatives, Kromos Technical Report 4,
2001. |
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5. Mathew Cushman: Image Compression, Kromos Technical Report 5, 2001. (most of it contained in
7 below) |
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6. Aleksandar Ignjatovic: Local Approximations and Signal Processing, Kromos
Technical Report 6, 2001. |
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PAPERS |
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2001 |
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7. M. Cushman: A Method for Approximate Reconstruction from Filter Banks,
SIAM Conference on Linear Algebra in Signals, Systems and Control, Boston,
2001. |
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8. T. Herron: Towards a New
Transform Domain Adaptive Filtering Process Using Differential Operators and
Associated Splines, International Symposium on Intelligent
Signal Processing and Communication Systems (ISPACS), Nashville, 2001. |
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9. J. Byrnes: Local Signal
Reconstruction via chromatic differentiation Filter Banks, 35th Asilomar
Conference on Signals, Systems and Computers, Monterey, 2001. 568–572. |
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10. P. P. Vaidyanathan, A.
Ignjatovic, and M.J. Narasimha: New sampling
expansions of band limited signals based on chromatic
derivatives, 35th Asilomar Conference on Signals, Systems and
Computers, Monterey, 2001., 558–562. |
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11.
A.
Ignjatovic: Numerical differentiation and signal processing, International Conference on Information,
Communications and Signal Processing (ICICS), Singapore, 2001. |
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2002 |
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12.
M. J. Narasimha., A. Ignjatovic, and
P. P. Vaidyanathan: Chromatic derivative filter banks,
IEEE Signal Processing Letters, 9(7),
2002, 215–216. |
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13.
M. Cushman, M. J. Narasimha, and P.P.
Vaidyanathan: Finite-channel chromatic derivative filter banks, IEEE
Signal Processing Letters, 10(1), 2002, 5–17. |
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2005 |
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14.
G. Walter and X. Shen: A
sampling expansion for non bandlimited signals in
chromatic derivatives, IEEE
Transactions on Signal Processing 53,
2005, 1291–1298. |
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2007 |
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15.
A. Ignjatovic: Local Approximations Based
on Orthogonal Differential Operators , Journal of Fourier Analysis and Applications, Vol.
13, Issue 3, 2007, pp. 309-330. (http://www.springerlink.com/content/d361x28401571112/fulltext.pdf
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16.
G. Walter: Chromatic
Series and Prolate Spheroidal
Wave Functions, preprint. Condensed version
to appear in the Journal of Integral Equations and Applications; see 17. 2008 17.
G. Walter: Chromatic Series With Prolate Spheroidal
Wave Functions,
Journal of Integral Equations and Applications, Volume 20, Number 2, 2008. 18. A. Ignjatovic: Chromatic
derivatives and local approximations, IEEE Transactions on Signal Processing,
Volume 57, Issue 8, 2009. 2009 19.
A. Ignjatovic: Chromatic Derivatives, Chromatic Expansions
and Associated Spaces, East Journal on Approximations, Volume 15, Number
3 (2009), 263-302. |
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PATENTS |
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US
Patent 6115726: Aleksandar Ignjatovic: Signal
processor with local signal behavior. This patent introduces the notion of chromatic derivatives, but
the expansions use polynomials as interpolation functions. Provisional Patent Disclosure 60/061,109 for this
patent was filled October 3, 1997. Patent application 09/144,360 for this
patent was filled May 28, 1998. The patent was issued September 5, 2000. |
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US Patent 6313778: Aleksandar
Ignjatovic and Nicholas Carlin: Method and a system
of acquiring local signal behavior parameters for representing and processing
a signal.
This patent introduces chromatic expansions and describes basic
signal processing methods based on chromatic expansions. Provisional Patent Disclosure 60/143,074 for this
patent was filled July 9, 1999. Patent application 09/614,886 for this
patent was filled July 9, 2000. The patent was issued November 6, 2001. |
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US
Patent 6587064: M. Cushman and A. Ignjatovic: Signal Processor with Local Signal Behavior and Predictive
Capability. This patent describes some prediction filters based on chromatic
expansions Patent application 09/897,325 for this patent was
filled July 2, 2001. The patent was issued July 1, 2003. |
SOFTWARE, ETC (if you need help, please feel free to email me!)
1.
Filter
coefficients for 129 tap transversal filters for twice oversampled signals for:
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Legendre chromatic derivatives
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Chebyshev chromatic derivatives
2.
Mathematica scripts for the Remez exchange filter design algorithm
used to produce the above filters