A note on misusing the interpolated FFT for real-valued sine wave

作者：Chen K Fu^*; Li Y; Fu Z Yi

来源：Mediterranean Journal of Measurement and Control, 2010, 6(2): 55-60.

• Coherent sampling
• Envelope line
• Fence effect
• Negative frequency
• Picket-fence effect
• Sine-wave
• Spectral line
• Spectrum leakage
• Window function

It has been reported in literature that the picket-fence effect of the Fast Fourier Transform (FFT) could be subdued efficiently by the interpolated FFT. However, it is shown here that for a real-valued sine wave (as against a cisoid) there are circumstances where the interpolated FFT is more erroneous than the direct readings on the FFT spectral lines. The underlying reason is the mistake of selecting the second highest spectral line, which is due to the interference from the negative frequency. In this paper, it is demonstrated that, both numerically and theoretically, the misplacement more likely occurs when the sampling is close to, but not at, the coherent condition. Also, the misplacement probability decreases as the cycles in the record increase, and is bounded by two envelope lines, which are derived theoretically.

• 出版日期2010
• 单位中国农业大学