Chromatic
Derivatives and Chromatic Approximations Home Page Last update
22/10/2010 What are the chromatic derivatives? You
can read about the theory of chromatic derivatives in the extended abstract
or introduction of this
paper or look at this practical,
hands-on interactive Mathematica tutorial/implementation
or
.pdf version |
TUTORIALS 1. Frequency estimation using chromatic
derivatives, Mathematica
Tutorial/implementation, ideal
for engineers who want to learn about the chromatic
derivatives, accompanying papers 2 and 3 below. This is a NEW
VERSION from July 8th ·
If
you do not have Mathematica you can
read the above tutorial by installing the free Mathematica
Player from the Wolfram’s website, or,
alternatively, you can look at the pdf of the above file.
·
Your
comments are most welcome; please email me at ignjat@cse.unsw.edu.au 2. Matlab version of the frequency estimation
code, still very crude and poorly commented, soon to be cleaned up: 1.
Eigensystem Decomposition based method Some
questions on
chromatic derivatives can be found here. 3.
A. Ignjatovic and A. Zayed: Multidimensional chromatic derivatives and series expansions,
to appear in the Proceedings of the American Mathematical Society. 4.
A.
Ignjatovic: Frequency
estimation using time domain methods based on robust differential operators,
the 10th IEEE International Conference on Signal Processing
(ICSP), 26 – 28 October 2010, Beijing, China. 6. A. Zayed: Generalizations of Chromatic
Derivatives and Series Expansions,
IEEE Transactions on Signal Processing, Volume 58 , Issue
3, 2010, 1638-1647 7.
A.
Ignjatovic: Chromatic
Derivatives, Chromatic Expansions and Associated Spaces,
East Journal on Approximations, Volume 15, Number 3 (2009), 263-302. |
11. G.
Walter and X. Shen: A sampling expansion for non bandlimited signals in chromatic derivatives, IEEE Transactions on Signal Processing 53,
2005, 1291–1298. |
|
|
2001 |
14. M. Cushman: A Method for Approximate Reconstruction
from Filter Banks, SIAM Conference
on Linear Algebra in Signals, Systems and Control, Boston, 2001. |
18. A. Ignjatovic: Numerical
differentiation and signal processing, International Conference on Information, Communications and Signal
Processing (ICICS), Singapore, 2001. |
Note: All of these patents are now in the public
domain, free to use! |
·
US Patent 6115726: Aleksandar Ignjatovic: Signal processor with local signal
behavior. |
·
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 describes some
prediction filters based on chromatic expansions |
SOFTWARE, ETC (if you need help, please feel free to email me!) more implementations to come soon!
1.
Filter
coefficients for 129 tap transversal filters for twice oversampled signals for:
· Legendre chromatic derivatives
·
Chebyshev chromatic derivatives
2. Mathematica scripts for the Remez exchange filter design algorithm used
to produce the above filters.