Abstract: A process for eliminating the Gibbs phenomenon in a train of digital signals when such signals are undergoing a discrete Fourier transform or a fast Fourier transform without using conventional windowing techniques wherein the train of digital signals is monitored and terminated when the last received or digital signal data point is equal to, or within a predetermined tolerance limit of, the first received digital signals so that the waveform of the train of digital signals reaches a complete periodicity within its length whereby no spurious frequency components will arise due to the Gibbs phenomenon. The process is shown as used in an all-purpose and multi-functioning digital filter.

Abstract: A process for suppressing the Gibbs phenomenon in a train of digital signals when such signals are undergoing a discrete Fourier transform or a fast Fourier transform without using the conventional windowing techniques wherein the original function defined by the initial set of digital signals is changed into a new function so that the first and last data points thereof are made equal to make the waveform of the new function each a complete cycle within its DFT period while the interrelationship of the remaining data points remain as in the original function, so that no spurious frequency components are introduced in the digital signal output. The process is shown as used in an all-purpose digital filter.