Lanczos filtering is a Fourier-based method for filtering digital data. Its key feature is the use of "sigma factors" that significantly reduce the amplitude of Gibbs oscillations. The method involves determining filter response quality using two graphs based on the number of weights and cutoff frequency. Examples of response functions in one and two dimensions are provided, along with comparisons to other filters. The simplicity of calculating weights and adequate response make Lanczos filtering an attractive method. The filter response function is expressed as an infinite Fourier series, with weights as Fourier coefficients. In practice, a finite series is used, leading to Gibbs oscillations if a step change in response is desired. Lanczos showed that truncating the series introduces a "modulated carrier wave," which can be suppressed by convolving a rectangular function with the response function. This results in a smoothed response function with weights determined by multiplying the original weight function by a sigma factor. The methodology is extended to two dimensions, with the response function expressed as a double sum over spatial frequencies. The weight function is derived from the ideal response function, modified by sigma factors. The two-dimensional Lanczos filter is shown to have a response function that can be determined using cutoff frequencies and the number of weights. The paper compares Lanczos filtering with other filters, such as the running mean and von Hann filters, showing that Lanczos filtering provides better response characteristics. It also compares Lanczos band-pass filtering with a Craddock filter, demonstrating that Lanczos filtering is easier to implement and yields good response characteristics. The paper concludes that Lanczos filtering is a simple and effective method for filtering digital data, with applications in both one and two dimensions. A computer program is available for calculating the weight function and response function. The research was supported by various funding agencies.Lanczos filtering is a Fourier-based method for filtering digital data. Its key feature is the use of "sigma factors" that significantly reduce the amplitude of Gibbs oscillations. The method involves determining filter response quality using two graphs based on the number of weights and cutoff frequency. Examples of response functions in one and two dimensions are provided, along with comparisons to other filters. The simplicity of calculating weights and adequate response make Lanczos filtering an attractive method. The filter response function is expressed as an infinite Fourier series, with weights as Fourier coefficients. In practice, a finite series is used, leading to Gibbs oscillations if a step change in response is desired. Lanczos showed that truncating the series introduces a "modulated carrier wave," which can be suppressed by convolving a rectangular function with the response function. This results in a smoothed response function with weights determined by multiplying the original weight function by a sigma factor. The methodology is extended to two dimensions, with the response function expressed as a double sum over spatial frequencies. The weight function is derived from the ideal response function, modified by sigma factors. The two-dimensional Lanczos filter is shown to have a response function that can be determined using cutoff frequencies and the number of weights. The paper compares Lanczos filtering with other filters, such as the running mean and von Hann filters, showing that Lanczos filtering provides better response characteristics. It also compares Lanczos band-pass filtering with a Craddock filter, demonstrating that Lanczos filtering is easier to implement and yields good response characteristics. The paper concludes that Lanczos filtering is a simple and effective method for filtering digital data, with applications in both one and two dimensions. A computer program is available for calculating the weight function and response function. The research was supported by various funding agencies.