| Recent yeats, with the development of DSP and microprocessor, it has been an important research trend to perform the advanced analysis to the digital signal with the employ of digital instruments and PC-instruments. By the digital and intelligent analysis of the digital signal with the theory and methodology of DSP, more exact and intuitionistic results can be achieved than the traditional measurements and instrumentation. As the development of DSP can provide the essentially improved hardware platform, it is significant to study on the corresponding measurement theory and methodology, especially the theory of digital signal processing. The measurement of noisy multifrequency signal parameters is one of an important subject in the field of instrumentation and measurements. The subject of multifrequency signal detection is mainly concerned with the signal retrieval from the noisy observation. Aimed on this research theme, this thesis studies thoroughly several key issues of multifrequency signal detection theory and its applications. The main contributions of the thesis are given as follows:1.In the case of long sample records, a new algorithm based on the Blackman windowing operation in time domain and interpolation in frequency domain is proposed. The ability of detecting weak harmonics and frequency resolution of this method can be improved remarkably;2.In the case of short record length and low SNR, a new method for sinusoidal detection is presented based on the SVD of the observation data matrix. By decomposing reasonably the Hankel data matrix constructed by the measured data, the method here can retrieve the signal from noise background effectively and has the superiority of high frequency resolution, stable computation and not be so sensitive to the level of noise;3.In the case of short record length and high noise level, a new method based on the criterion of TLS is proposed. By solving an over-determinate equation system with TLS criterion, the method here can eliminate the noisy perturbation of observation data matrix effectively to achieve much more exact results;4.An improved approach is proposed for the sinusoidal retrieval in the presence of prior knowledge. A simple iteration algorithm is adopted to eliminate the known frequencies in the observations. By incorporating the prior knowledge effectively, more exact approximation results than traditional approach can be achieved, which is verified by the simulation experiments;5.A kind of non-parametric model spectral analysis method, i.e., MTSA is studied and an MSMTSA estimator is built based on the minimization of a cost function. It is indicated by the performance analysis that the approach here has comparative bias and variance as the approach of DPSS-MTSA. Compared with the DPSS, the MS-MTSA method here needs less calculation efforts with the intuitionistic and analytical expression of sinusoidal tapers;6.Based on the MS-MTSA method above~ a new approach for the detection of harmonic in colored noise is proposed. With the theory of hypothesis test, the sine spectral estimator can be used to detect the harmonics and to estimate the parameters exactly. By eliminating the estimated part of signal from the observation, a spectral estimation to the background colored noise can be obtained at the same time. The experimental result shows the high performance of bias and variance of this approach.
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