Blur filters work by convolving an image with a kernel that averages neighboring pixel values. Box filters treat all neighbors equally, causing artifacts because their frequency-domain representation has blocky patterns that fail to suppress certain high frequencies. Gaussian filters weight pixels by distance from center, and their Fourier transform is also Gaussian — a smooth low-pass filter that cleanly removes high-frequency components. The convolution theorem shows that convolution in the spatial domain equals multiplication in the frequency domain, explaining why Gaussian blur is smoother. Practical implementation uses discrete Gaussian sampling, binomial filter approximations (which have integer coefficients for hardware efficiency), and separable 2D filtering (applying 1D filters along each axis separately) for performance.
Sort: