The paper introduces Lanczos filtering, a Fourier method for filtering digital data that significantly reduces the amplitude of Gibbs oscillations through the use of "sigma factors." The method involves modifying a data sequence with a set of weights to produce a new sequence, with the filter response function determined by the Fourier transform of the weight function. Lanczos filtering is particularly effective in reducing Gibbs oscillations by convolving the ideal response function with a rectangular function and multiplying it by a sigma factor. The paper presents graphs that predict the main characteristics of the response function based on the number of weights and the cutoff frequency. Examples of response functions in one and two dimensions are provided, and comparisons are made with other filters. The simplicity of calculating the weights and the adequate response make Lanczos filtering an attractive method. The methodology is extended to two-dimensional filtering, and a computer program is available for calculating the weight and response functions.The paper introduces Lanczos filtering, a Fourier method for filtering digital data that significantly reduces the amplitude of Gibbs oscillations through the use of "sigma factors." The method involves modifying a data sequence with a set of weights to produce a new sequence, with the filter response function determined by the Fourier transform of the weight function. Lanczos filtering is particularly effective in reducing Gibbs oscillations by convolving the ideal response function with a rectangular function and multiplying it by a sigma factor. The paper presents graphs that predict the main characteristics of the response function based on the number of weights and the cutoff frequency. Examples of response functions in one and two dimensions are provided, and comparisons are made with other filters. The simplicity of calculating the weights and the adequate response make Lanczos filtering an attractive method. The methodology is extended to two-dimensional filtering, and a computer program is available for calculating the weight and response functions.