Haar Wavelet Decomposition Source Code

This text discusses the source code implementation for Haar wavelet decomposition, mentioning it twice for emphasis. To provide more comprehensive technical context, we expand on the algorithm's fundamental principles. Haar wavelet decomposition represents a widely adopted signal processing technique that decomposes signals into sub-signals at different frequency bands. The algorithm operates through iterative averaging and differencing operations, where each decomposition level splits the input signal into approximation coefficients (low-frequency components) and detail coefficients (high-frequency components). From an implementation perspective, the core logic involves: 1. Applying a pair of filters - the scaling function for approximations and the wavelet function for details 2. Downsampling the filtered outputs by a factor of 2 3. Recursively processing the approximation coefficients for multi-level decomposition Practical applications span image processing (edge detection, compression), data compression, and feature extraction. Through Haar wavelet decomposition, engineers can effectively separate signal details from approximate representations, enabling deeper analysis of signal characteristics and structural patterns. Mastery of the Haar wavelet source code is therefore essential for signal processing engineers and researchers, particularly for custom implementations requiring modifications to decomposition levels, boundary handling, or coefficient thresholding.