From: http://blog.sina.com.cn/s/blog_4af018020100ef2k.html
Fence Effect : For the spectrum of Sampled Signals, FFT is usually used to improve the computing efficiency. Algorithm For calculation, set the number of data points
N = T/dt = T. FS
The calculated discrete frequency point is
Xs (FI), FI = I. fs/N, I = 0, 1, 2 ,..., N/2
This is equivalent to viewing the landscape through a fence. only part of the spectrum can be seen, while other frequency points cannot be seen. Therefore, some useful frequency components may be missed. This phenomenon is called the fence effect.
Both time-domain sampling and frequency-domain sampling have corresponding fence effects. Only when the time-domain sampling satisfies the sampling theorem, the fence effect will not be affected. The fence effect of frequency-domain sampling has a great impact. Blocking or loss of frequency components may be important or characteristic components, making signal processing meaningless.
Reducing the fence effect can be solved by increasing the sampling interval, that is, the frequency resolution. The interval is small and the frequency resolution is high. The smaller the frequency component that is blocked or lost. However, the number of sampling points is increased to increase the computing workload. To solve this problem, the following methods can be used: When the sampling theorem is met, the frequency refinement Technology (zoom) can also be used to convert the time domain sequence into a Spectrum Sequence.
For example : Spectrum Analysis of a 50-5Hz sine wave signal is used to describe the spectrum calculation error caused by the fence effect.
Set the sampling frequency fs = 5120Hz. The default FFT calculation point in the software is 512, and its discrete frequency point is
FI = I. fs/N = I .5120/512 = 10 × I, I =, 2 ,..., N/2
The actual peak at the 505Hz location is blocked and invisible, only the values of energy leakage at the adjacent frequency of Hz or Hz are seen.
If FS is set to 2560Hz, the frequency interval DF is 5Hz. Repeat the above analysis steps and there is a spectral line at the 505 position. Then we can get their exact values. In the time domain, this condition is equivalent to full-cycle sampling of signals. In practice, this method is often used to improve the accuracy of spectrum analysis of periodic signals.
Spectrum leakage: The Truncation signal is multiplied by the rectangular window in the time domain, resulting in spectrum leakage. What I see in the post: http://www.chinavib.com/forum/thread-51126-2-1.html The reason for the leakage is that the first input frequency is not an integer multiple of FS/N, because DFT can only output the power at the FS/N frequency point, therefore, when the input frequency is not an integer multiple of FS/N, the output of DFT does not correspond to the input frequency (the output of DFT is discrete ), then the input frequency will leak to all the output points. The specific Leakage Distribution depends on the continuous domain compound leaf transformation of the used window. For those without a window, it is equivalent to using a rectangular window, rectangular window in the continuous Fourier transformation in the general signal and system books have. But for non-rectangular windows, the window itself will produce a certain degree of leakage, by increasing the width of the main flap to reduce the amplitude of the Side Lobe. Generally, the width of the main flap is twice that of the rectangular window, for example, when we input an integer multiple of the FS/N input frequency, after a non-rectangular window, the DFT output will have power at two FS/N frequency points.
See the reference book: Lyon understanding DSP. Side-lobe effect: Influence of zero padding on the spectrum: the zero padding only increases the data length, not the original signal length. It is like if the original signal is a periodic cosine signal, and if it is supplemented with nine periods of length 0, then the signal is not the cosine signal of ten periods, instead, the cosine of a period adds a string of 0, and the supplemented 0 does not bring new information. In fact, zero padding is equivalent to the Sinc function interpolation in the frequency domain, and the shape (main flap width) of this sinc function is determined by the signal length before 0, the function of complementing 0 only refines the Sinc Function and does not change the width of the main flap. The definition of frequency resolution is that two signals with different frequencies can be divided on the frequency, which requires that they cannot be placed on the main valve of an sinc function. Therefore, if the two signal frequencies to be analyzed are close to each other, and the time domain length is short, they will fall into an sinc primary valve in the frequency domain, and it will be useless to add more zeros.
