Gabor Equation Function

The Gabor equation function I developed serves as a versatile tool for generating overcomplete sparse representation dictionaries. This implementation utilizes a mathematical framework that combines Gaussian envelopes with complex sinusoidal carriers, allowing flexible control over filter orientations, scales, and frequencies through parameterized inputs. The resulting dictionary finds applications across multiple domains including signal processing (through time-frequency analysis), image processing (via texture feature extraction), and audio processing (for spectral decomposition). The function's architecture supports customizable filter bank generation, where users can specify parameters like bandwidth, center frequencies, and spatial aspect ratios to optimize sparse coding performance. Additionally, this function provides researchers with deeper insights into signal characteristics and properties through its adjustable atom generation mechanism, enabling improved research outcomes in sparse coding and dictionary learning applications. The implementation includes optimization features for computational efficiency while maintaining mathematical precision in atom construction. Overall, this function represents a practical and adaptable solution applicable across diverse technical domains and implementation scenarios.