The discrete Fourier transform with reduced spectral leakage and its applications in image processing

• Main Authors: Yu-Che Wen, 温育哲
• Other Authors: Senfar Wen
• Format: Others
• Language: zh-TW
• Online Access: http://ndltd.ncl.edu.tw/handle/6qgmex

碩士 === 元智大學 === 光電工程學系 === 103 === Discrete Fourier transform (DFT) calculates the spectrum of a signal. The computation cost of DFT can be effectively reduced by the use of the fast Fourier transform (FFT) algorithm. The frequency sampling of FFT is equally spaced. When a signal comprises a frequency which is not just equal to one of the equally spaced frequencies, the amplitude of the signal frequency spreads to all the frequency components. This phenomenon is called the spectral leakage or DFT leakage. There are no methods can calculate the accurate spectrum for such a case in state of the art. This thesis proposes a method for reducing the DFT leakage. The proposed method is able to calculate the accurate spectrum of the signal with isolated frequency components. For the signal without such a characteristic, the calculated spectrum may not be accurate but its DFT leakage can be reduced. The applications of this method to image processing are taken as examples.