Design 0f a Windowless Digital Filter Using Fft Algorithm*

The Gibbs phenomenon appears in a discrete Fourier transform due to incomplete periodic@; i. * e., the waveform has not reached a full cycle within its period. Data flipping furnishes a complete periodic cycle to the waveform and thus suppresses the Gibbs phenomenon. This facilitates the design of a digital filter using fast Fourier transform without windowing. The filter does lowpass, bandpass, highpass, bandstop, notch, or single-frequency-pass simply by manipulating the band limits. The filter can be affected by spectral resolution and the slope discontinuity at the end data points. The reduction of such effects and an alternative design are discussed. Submitted to IEEE Transactions on Signal Processing * Work supported by Department of Energy contract DE-AC03-76SF005 15.