Gibbs phenomenon removal and digital filtering directly through the fast Fourier transform

Author

Pan, Cheh

Author_Institution

Pan Filter Technol., Saratoga, CA, USA

Volume

49

Issue

2

fYear

2001

fDate

2/1/2001 12:00:00 AM

Firstpage

444

Lastpage

448

Abstract

The Gibbs phenomenon in the Fourier transform is due to a periodicity discrepancy between the waveform and its sinusoidal representations in the time domain. Data flipping, baseline tilting, or digital comparison completes the periodicity of the waveform and thus removes the Gibbs phenomenon. This facilitates digital filtering directly through the fast Fourier transform. Such a filtering is unique and exact, with its stop-band totally zeroed out and passband fully passed. It accomplishes lowpass, bandpass, highpass, bandstop, notch, or single-frequency-pass simply by manipulating the band limits

Keywords

digital filters; fast Fourier transforms; filtering theory; waveform analysis; Gibbs phenomenon removal; bandpass filtering; bandstop filtering; baseline tilting; data flipping; digital filtering; fast Fourier transform; highpass filtering; lowpass; notch filtering; single-frequency-pass filtering; sinusoidal representation; time domain; waveform periodicity; Band pass filters; Convolution; Digital filters; Discrete Fourier transforms; Fast Fourier transforms; Filtering theory; Frequency domain analysis; Frequency response; IIR filters; Passband;

fLanguage

English

Journal_Title

Signal Processing, IEEE Transactions on

Publisher

ieee

ISSN

1053-587X

Type

jour

DOI

10.1109/78.902128

Filename

902128