Computation of 1D and 2D Convolution

Computation of one-dimensional and two-dimensional convolution represents a fundamental technique widely applied in signal processing and image processing domains. This mathematical operation serves as the core mechanism for various applications including filtering, edge detection, and blurring effects. In MATLAB environments, convolution operations are typically implemented using the built-in conv (for 1D signals) and conv2 (for 2D images) functions. The algorithm implementation follows the mathematical definition where each output element equals the sum of element-wise products between the input signal and reversed kernel elements, requiring nested loops for kernel traversal. When migrating algorithms to other programming languages, C language provides optimal efficiency through direct memory manipulation and pointer arithmetic. For 1D convolution, the implementation typically involves a sliding window approach with O(n*m) complexity, while 2D convolution requires double loops for both row and column directions. The code structure emphasizes modular design with separate functions for boundary handling (zero-padding or symmetric extension) and kernel normalization, ensuring straightforward adaptation to real-time systems or embedded platforms.