Phase Transmission Characteristics of Temporal Windows in Fourier Transformation

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  • フーリエ変換における窓関数の位相特性
  • フーリエ ヘンカン ニ オケル マド カンスウ ノ イソウ トクセイ

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In harmonic analysis of periodic wave, the discontinuity at the boundary of observation interval increases the spectral leakage. Several temporal windows have been developed to improve the spectral resolution. In Fourier transformation, input signal is transformed into complex data consisting of amplitude and phase. This paper describes the phase transmission characteristics of temporal windows. The phase preservability that the phase of input sinusoidal wave is preserved in peak component, can be improved by applying the windows. Phase error caused by the other harmonics depends on the amplitude transmission characteristics of windows, especially on their band-width. The spectral peak moves from n-th bin to (n+1)-th bin with the increase of input frequency. The frequency, at which the peak is shifted from n to n+1, becomes close to n+0.5 through temporal windows. Experiments of pitch-frequency detection using phase compensation method show that Hanning window and Cos window are more desirable than the others.<br>As a result, the temporal window improves the phase transmission characteristics.

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