Signals Frequency Estimation Based On Two Dimension Amplitude Spectrum

When signals were truncated by non-integer period or signals contained noise, the typical amplitude spectrums would produce spectrum leakage and reduced the accuracy of signals frequency estimating. To change this condition, this paper extended the amplitude spectrum of signals from one dimension to two on the basic conception and calculation formula of typical DFT, and gave a new mode of signals frequency spectrum which could show us more useful information of signals and not be restricted by integer period truncating. The characters of 2D spectrum compared with 1D’s are shown as follows:1. The length of signals which would be used to produce 2D spectrum is not limited by integer period truncating. As we all know, spectrum leakage will make people not read the useful information easily from 1D amplitude spectrum, and people also cannot recognize the main spectrum lines among the all spectrum lines from the 1D ones when signals are truncated by non-integer period or contain noise. The 2D spectrum’s theory is on the base of DFT formula, which considered both the signal length N and frequency point k as variables. So, to a limited signal, all frequencies will have a chance to be truncated by integer period. Thereby, the 2D spectrum included both the non-integer period points and integer period points and could show us more useful information than 1D ones.2. The 2D spectrum is anti-noise. When the SNR is -10dB, the 2D spectrum even can show people the position of energy concentrated all the same, not only to the sine signals, but also to the multi-frequency ones.3. From the 2D spectrum, people can read more useful information of signals. To compare with 1D spectrum, people could know the frequency construction from the 2D ones, which can tell us not only how many frequencies the signal contained and but also the amplitudes of signals. When people rotated the 2D spectrum, they could know the amplitude changing law which is 1D spectrum namely when the amplitude changing along with the frequency point k changing , and the changing law of amplitude which followed sinc function when the amplitude changing along with the length of truncated signals changing.On the base of 2D spectrum, this paper brought the image processing method to the signal processing field and put forward a new method of frequency estimation. Firstly, make a pre-treatment to the 2D spectrum by image processing method; secondly, estimate the period T of the every frequency of signal on the base of 2D spectrum which had be pre-treated; finally, calculate the frequency f according to the quantitative relation among sampling frequency f s, signal frequency f and period T.This paper made use of some typical signals to do a series of experiments to proof the validity of the method and get conclusion as follows:1. This method is anti-noise. This method could estimate the frequency of sine signals accurately When the SNR is -10dB, and the method could estimate every frequency of multi-frequency signals truly when the SNR is low. Because the 2D spectrum is anti-noise, so the method which is on the base of 2D spectrum is anti-noise.2. This method has high precision. When there are signals which do not contain noise, the lowest error of frequency estimation could get to zero to the sine signals, and the error of seventh frequency is 2.8‰to the saw-teeth wave signals which contained seven harmonic wave components. To the sine signal which SNR is -10dB, the error of frequency estimation is approximate to 2.6﹪. And to the saw-teeth wave, in which, the error of the seventh frequency components is 1.4‰when the SNR is 4dB. The method could correctly estimate the frequency of every harmonic component of signals.This paper extended the conception and calculations of Discrete Fourier Transformation from one dimension to two, and give a new expression of signal frequency spectrum. The estimating method on the base of 2D spectrum spent a little time on calculating but could estimate signals’frequency in a high precision and provided people a new reference to signal frequency estimating.