Spectral Signal Processing Suite, version 1.0 (2003)

The Spectral Signal Processing Suite (SSPS), version 1.0, is for the purpose of increasing the accuracy of discrete Chebyshev approximations of discontinuous functions by reducing or eliminating the Gibbs-Wilbraham phenomenon. The suite may be used to implement a postprocessing method for the Chebyshev Collocation (Pseudospectral) or Chebyshev Spectral Viscosity methods for solving Partial Differential Equations. The suite implements spectral filtering, edge detection, and Gegenbauer Reconstruction postprocessing algorithms.

The Spectral Signal Processing Library is written the Java programming language and has a graphical user interface which conveniently wraps the numerical classes and provides a graphical examination of the edge detection and postprocessing process. All source code is freely available and the library may be used in any way that is desired as long as links/references to this page are clearly provided in any work which uses the library or in any software that incorporates or extends the Spectral Signal Processing Suite. The Spectral Signal Processing Suite comes with absolutely no warranty of any kind. Bug reports and coding suggestions are welcome and should be sent to scott@ScottSarra.org. Descriptions of the algorithms implemented in the software and examples using the software can be found in the paper The Spectral Signal Processing Suite which appears in the ACM Transactions on Mathematical Software, vol. 29, no. 2, June 2003.

Demo Applet/documentation

• Applet (optimized for 1024x768 screen size).  Here is a newer applet running version 1.5 which now implements edge detection and postprocessing for Fourier data. 
• Graphical User Interface Guide (guiGuide.pdf)
• Documentation (javadoc files)

Installation

• Download signal1_0.jar and place in a directory of your choice, e.g. c:\jp\signal1_0.jar. Modify your classpath variable to find the package. At the DOS or shell prompt enter set classpath=c:\jp;
• Set up a directory for your application, say c:\j\postProcess. Modify the pp.java so that the setDataDirectory( ) method sets the data loading/writing directory to the directory of your choice. To run the application type java -cp signal1_0.jar pp at the prompt.

Source Code

• pp.java
• chebyshevPolynomial.java, edgeDetect.java, edgeDetectAB.java, gegenbauerPolynomial.java, gegenbauerReconstruction.java, gegenbauerReconstructionB.java, hybrid.java, hybridB.java

Postprocessing papers

1. The Spectral Signal Processing Suite, ACM Transactions on Mathematical Software, vol. 29, no. 2, June 2003.
2. Spectral Methods with Postprocessing for Numerical Hyperbolic Heat Transfer. Numerical Heat Transfer A, 43 no. 7 (2003), pp. 717-730.
3. Chebyshev Super Spectral Viscosity method for a Fluidized Bed Model. Journal of Computational Physics, 186/2, p. 630-651 (2003).
4. Digital Total Variation Filtering as Postprocessing for Pseudospectral Methods for Conservation Laws.  Numerical Algorithms, vol. 41, p. 17-33, 2006.
5. Digital Total Variation Filtering as postprocessing for Radial Basis Function Approximation Methods.  Computers and Mathematics with Applications, vol. 52, p. 1119-1130, Sept. 2006