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Fence Effect in FFT Spectrum


To reduce amount of computation, we usually use FFT technique to compute the spectrum of  a signal. If the length of the FFT is:
.              N = T/dt = T.fs
We can only get the spectrum value in certain frequency point:
.              Xs(fi) £¬ fi = i.fs/N , i = 0£¬1£¬2£¬.....£¬N/2
This is like to see behind a fence, so it is called the fence effect of  FFT. For example, If we sample a 100Hz sine signal with 5000Hz and do a 1024 FFT. The spectrum line is located in:
.                            0Hz, 4.88Hz, 9.76Hz,...............2500
There is no spectrum line in 100Hz, we can't see it. We can only see it's leakages in 97.6Hz and 102.48Hz. These result in two error, one is frequency error, another is amplitude error. If we sample the signal  with 5120Hz and do a 1024 FFT. The spectrum line is located in:
.                            0Hz, 5Hz, 10Hz,...............2560
There is a spectrum line in 100Hz, we can measure it accurately. This is called integer period sampleing and can be used to the fence effect of FFT. It is commonly used in the measure of rotating machinery.

The applet can produces a sine signal, then shows its FFT spectrum and a zoom continue Fourier spectrum. You can see the fence effect of FFT by compare of them.
Java Learning Program
 

Fence Effect in FFT
Usage:
1.Input Frequency, Amplitude and phase of a sine signal.
2.Press "Generate" to produce this signal and show its spectrum,
3.Change a sample frequency that has spectrum line on the signal frequency, Press "Generate" to produce the signal and show its spectrum again.

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