Optimal Window Design by Linear Programming

This section, based on a class project by EE graduate student Tatsuki Kashitani, illustrates the use of linprog in Matlab for designing variations on the Chebyshev window. In addition, some comparisons between standard linear programming and the Remez exchange algorithm (firpm) are noted. For Matlab source files, etc., see
http://www.stanford.edu/~tatsuki/MUS421/lp_presentation/.

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Subsections

• Linear Programming (LP)
• Matlab's LINPROG
• LP Formulation of Chebyshev Window Design
• Symmetric Window Constraint
• Positive Window Sample Constraint
• DC Constraint
• Sidelobe Specification
• Sidelobe Specification (cont.)
• LP Standard Form
  • Normal Chebyshev Window
  
  
• Remez Exchange Algorithm
  • Convergence of Remez Exchange
  
  
• Monotonicity Constraint
  • Monotonic Chebyshev Window
  
  
• L-Infinity Norm of Derivative Objective
• L-One Norm of Derivative Objective

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Order a Hardcopy of Spectral Audio Signal Processing

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.