Study On Sinusoid Signal Harmonic Retrieval Using The Cyclic Cross-cumulant Estimation Method

Recently, we have made great progress in the estimation of weak signal innoises. Such as spectral estimation applies cross-spectral theory and high-orderself-spectral theory up to now, but they have flaw is applied separately. SoCross-high-order cumulant method based on high-order cumulant and cross-spectral estimation .The cross-high-order-cumulant (CHOC) such as thecyclic-cross-cumulant is firstly proposed to measure both the sinusoids signalparameter estimation and the estimation from the colored noises .Sinusoid signal is a very important signal in digital signal processingcommunity. It is widely used in many systems, e.g: communication, radar, sonar,seismography, geology and bioengineering. The research on Sinusoids signal is ofsignificance in both signal processing theory and its practice applications.The work of this paper includes one primary question: parameter estimation ofsinusoids signals. Various techniques have been used to perform sinusoids signalsparameter estimations, but they almost have disadvantages of high complexity andhuge computational cost, the other shortcoming is that the additive noise of thesemethods must be restricted in Gaussian noise. The mature approaches are mostlybased on assume of stationary model. The excellent methods of sinusoids signaltime delay estimation are even less. To solve these questions, here we propose a setof new sinusoid signal processing methods based on the cyclic cross-cumulant.In parameter estimation domain the initialization frequency is estimated,Based on the analysis of signal and the additive noise .cyclic-cross-correlationfunction method and the cyclic-cross-cumulant method are proposed . Chapter fourpresents the emulation conclusion of the two methods and testify the correctnessand the validity of the new approaches based on multiple Sinusoids signals areeffective to estimation from the colored noises. The new approaches pass highresolution and stability, computational costs are also small.The main tasks are generalized as:1. The structure of Sinusoids signal is analyzed and a set of new sinusoidssignal processing methods are proposed: The nonstationary sinusoids signals areestimated by the cyclic cross –cumulant method.2. Based on the analysis of Sinusoids signals and the additive noise,cyclic-cross-cumulant method suitable for Sinusoids signal parameter estimation isbrought forward. Then the third-order -cyclic-cross-cumulant function and cycliccross-correlation function are discovered.3. The cyclic-cross-correlation function and third-order-cyclic-cross-cumulantfunction are gained by the temporal cross-correlation function and temporalcorss-cumulant function, characters are studied profoundly. Chapter four presentsthe emulation conclusion of the three methods and contrasts them to thecross-higher-order method to testify the correctness and the validity of the newapproaches.Compared with general approaches, the methods in this paper have manyprominent virtues:1. They have low complexity. Here we estimate directly nonstationary signal,which avoid the use of other complicated convert sinusoids signals into a kind ofstable state by quadratic form transformation processing methods.2. They have good noise-restrain ability, with the introduction of the cycliccross-correlation estimation and the third-order cyclic cross-cumulant estimation.3. They can get accurate estimation results even with short data sequences. Itmakes these methods more applicable to engineering practice.4. They all have high resolution and stability.Generalized speaking, we consider that the sinusoids signal parameterestimation methods proposed in this paper have academic significance andengineering applicable value. They are effective and can put into practice.