Second-Order Butterworth High-Pass Filter Implementation with Code Integration

This document demonstrates the implementation of second-order Butterworth high-pass filtering for image processing. Begin by placing the image file and program code in the same directory after extraction. The core algorithm involves designing a second-order Butterworth high-pass filter using transfer function coefficients, typically implemented through frequency domain transformation or digital filter design functions like butter() in MATLAB or scipy.signal.butter() in Python. The processing workflow includes converting the image to frequency domain using Fast Fourier Transform (FFT), applying the filter transfer function to attenuate low-frequency components while preserving high-frequency information, and performing inverse FFT to reconstruct the enhanced image. Key parameters like cutoff frequency can be adjusted through variables such as Wn in the filter design function to control the filtering intensity. This method effectively removes low-frequency noise and enhances image clarity by emphasizing high-frequency components like edges and textures. The filtered results will be displayed to demonstrate the visual improvement, showcasing applications in image enhancement, edge detection, and feature extraction. Practical implementation considerations include proper normalization of frequency values and handling of boundary artifacts through padding techniques. The code structure typically involves main functions for filter design, frequency domain operations, and result visualization through plotting libraries.