| Sinusoidal signal is simple in shape,easy to implement,and widely used in signal processing.In discriminating sinusoidal signals,the most important parameter is the frequency value,but in the process of signal transmission,the actual sinusoidal signal processing is usually polluted by noise.Therefore,how to strip the noise interference and estimate the main parameters of the original signal from the actual signal has become the research direction of signal processing in many fields.Over the years,there have been many excellent algorithms for frequency estimation,and the research results have been applied in many fields,including radar,electricity,voice,biomedicine,communication and so on.In these fields,the most popular problem is how to remove noise from narrowband interference signals and obtain the most valuable key parameter information.Signal parameter estimation algorithms can be roughly divided into two categories:time domain and frequency domain.However,currently commonly used algorithms are mainly focused on the frequency domain,and THE DFT algorithm is the basis of all frequency domain algorithms.In the actual calculation and calculation process,FFT has fewer calculation steps than DFT,so FFT is generally used to replace DFT.However,DFT algorithm has some inherent problems,mainly spectrum leakage and fence effect,so in order to eliminate the negative effects brought by these problems,it is necessary to add more steps in the algorithm deduction process.Based on the above background,this paper further analyzes how to estimate sinusoidal signal parameters more accurately,mainly including:Firstly,this paper deduces the mathematical expression of basic sinusoidal signals,including real sinusoidal and complex exponential signals,and further expounds how the two expression forms transform each other.The inherent problems of frequency domain analysis based on DFT are explained,including spectrum leakage and fence effect,and some evolutionary algorithms are proposed to improve the related problems.Then,this paper introduces the performance indicators of the estimated results:Bias,Variance and minimum mean square error(MSE),and deduces the best boundary of the measurement index-CRLB.At the same time,the parameter estimation algorithm of sinusoidal signal is also explored in order to better solve the inherent problems of parameter estimation.A parameter estimation method based on MDCT(Modified Discrete Cosine Transform)was proposed,which was different from the traditional algorithm.The formulas were deduced and simulated from the following aspects:(1)For complex sinusoidal signals which are not interfered by "negative frequency".Through strict mathematical formula derivation,the algorithm finally describes the relationship between MDCT value and system frequency through a ternary linear equation,and selects the first three maximum values according to the magnitude of absolute value of MDCT:X(k0),X(k0+1)and X(k0-1),simulation experiments for optimal frequency estimation.Finally,through MATLAB simulation,from the perspective of variance verification,noise interference and harmonic interference,it is proved that the algorithm proposed in this paper has excellent performance in anti-noise performance,accuracy,and anti-harmonic ability compared with other MDCT domain estimation algorithms,which proves that it can be applied in practical production applications.(2)For the real sinusoidal signal interfered by "negative frequency".Through strict mathematical formula derivation,the algorithm finally describes the relationship between MDCT value and system frequency through a ternary linear equation,and selects the first three maximum values according to the magnitude of absolute value of MDCT:X(k0),X(k0+1)and X(k0-1),simulation experiments for optimal frequency estimation.In addition,in order to make the algorithm more accurate,the sliding sequence method is adopted to eliminate the frequency instability caused by the initial random phase.Finally,through MATLAB simulation,from the perspective of variance verification,noise interference and harmonic interference,it is proved that the algorithm proposed in this paper has excellent performance in anti-noise performance,accuracy,and anti-harmonic ability compared with other MDCT domain estimation algorithms,which proves that it can be applied in practical production applications.(3)Aiming at the more common multi-complex sinusoidal signals in practical production and application,the algorithm deduces strict mathematical formulas,and finally describes the relationship between MDCT value and system frequency through P ternary linear equations.According to the absolute value of MDCT,the first three maximum values are selected for each complex sinu soidal signal:Xp(kmax(p)),Xp(kmax(p)+1)and Xp(kmax(p)-1),simulation experiments for optimal frequency estimation.Finally,through MATLAB simulation,it is proved that the algorithm proposed in this paper has excellent performance in accuracy and anti-harmonic ability from noise interference and harmonic interference,compared with other algorithms using MDCT domain estimation,which proves that it can be applied in practical production applications. |
