Image DCT High-Pass and Low-Pass Filter Implementation with Fourier Transform Comparison

We implement Discrete Cosine Transform (DCT) high-pass and low-pass filters for image processing and compare them with Fourier Transform (FFT) based filtering. The implementation involves calculating DCT coefficients using algorithms like dct2() in MATLAB or similar functions in Python's OpenCV/scipy packages, followed by applying frequency domain masks to preserve or eliminate specific coefficient ranges. From the experimental results, images processed with DCT low-pass filtering appear significantly blurred. This occurs because DCT essentially computes the real component of FFT, leading to energy reduction in the transformed domain. The filtering process typically involves zeroing out high-frequency DCT coefficients beyond a certain threshold, which results in smoother but less detailed reconstructions compared to FFT-based filtering that preserves complex frequency information. For DCT high-pass filtering, the implementation selectively removes low-frequency coefficients while preserving high-frequency components. This elimination of low-frequency information darkens the overall image, leaving only edge contours and high-contrast features visible. The code typically applies a binary mask to the DCT coefficient matrix, setting lower-frequency regions to zero while maintaining higher-frequency components for inverse transformation.