Tactile sensor array touchpad user interface (u.s. patent 6,570,078)
Six Degrees of Freedom from the Touch of a Finger Tip
Spatial Resolution and Parameter Derivation Stability
Applications to Music Keyboards: Timbre Control (U.S. Patent Application 2004/0074379)
Applications to Music Keyboards: Vocal Choir Synthesis (U.S. Patent Application 2004/0074379)
Gesture Recognition (Summer 2009)
Applications to South Asian Tabla and Baya Technique (Summer 2009)
Fractional fourier transform
Kernel Studies 1: Counter-Rotating Asymptotes of the Hyperbolic Quadratic Form
Kernel Studies 2: Contour Plot of the Hyperbolic Quadratic Form
Kernel Studies 2: Contour Plot of the Hyperbolic Quadratic Form
Kernel Studies 2: Contour Plot of the Hyperbolic Quadratic Form
Iso-Power View of Geometric Lens Optics
Focus Correction (U.S. Patent 6,687,418 and U.S. Patent 7,054,504)
through-zero pulse-width modulations
Centered-, Left-, and Right-Modulated Periodic Pulse Waveforms
Positive and Negative Relative Frequency Representations
Comparative Constructions of Through-Zero Pulse-Width Processes
symbolic dynamics of square waves
Symbol Definitions
Torus Representation and Frequency Comparison
Tiling Representation and Frequency Comparison
Symbolic Dynamics Frequency Comparator Implementation (Patent Pending)
sub-octave waveform cross products (u.s. patent 6,849,795 )
Sub-Octave Cross-Products of Square Waves
Sub-Octave Cross-Products of Triangle Waves
overtone tracking in music and performance systems (patent pending)
Harmonic Vibration with Time-Varying Overtone Amplitudes
Inharmonic Vibration with Time-Varying Overtone Amplitudes
Audio Synthesis Application Example
Stage Lighting Application Example