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Accurate Frequency Estimation Based On Three-Parameter Sine-Fitting With Three FFT Samples

Liu X., Ren Y., Chu C., Fang W.

Metrology and Measurement Systems

2015

Vol. 22, nr 3

403--416

This paper presents a simple DFT-based golden section searching algorithm (DGSSA) for the single tone frequency estimation. Because of truncation and discreteness in signal samples, Fast Fourier Transform (FFT) and Discrete Fourier Transform (DFT) are inevitable to cause the spectrum leakage and fence effect which lead to a low estimation accuracy. This method can improve the estimation accuracy under conditions of a low signal-to-noise ratio (SNR) and a low resolution. This method firstly uses three FFT samples to determine the frequency searching scope, then – besides the frequency – the estimated values of amplitude, phase and dc component are obtained by minimizing the least square (LS) fitting error of three-parameter sine fitting. By setting reasonable stop conditions or the number of iterations, the accurate frequency estimation can be realized. The accuracy of this method, when applied to observed single-tone sinusoid samples corrupted by white Gaussian noise, is investigated by different methods with respect to the unbiased Cramer-Rao Low Bound (CRLB). The simulation results show that the root mean square error (RMSE) of the frequency estimation curve is consistent with the tendency of CRLB as SNR increases, even in the case of a small number of samples. The average RMSE of the frequency estimation is less than 1.5 times the CRLB with SNR = 20 dB and N = 512.

Basic laws of aircraft design

Danov A.

ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes

2015

Vol. 4, No 3

91--97

Questions of attraction to tasks of aviation technical designing of the regularities of general nature which are earlier not used in this field which are on a joint of basic problems of modern natural sciences, technology, philosophy and the new directions of science which treat, for example, synergy, and others are considered. A conceptual design of civil and transport airplanes with representations of the seven basic laws of the design is offered: 1. Thought or mental associated with the formation of the idea, as well as the visualization of forms and structures designed object. 2. The law of analogies. 3. The Law of Vibration. 4. The law of opposites. 5. The law of cycles and rhythms. 6. The Law of Cause and Effect. 7. Law of design and creativity. The approach to formation of new hierarchy of the criteria of design based on the analysis and synthesis of these laws is also offered. The task of the structural formation and composition of the energy space design, allowing determining the grid of power lines and types of elementary energy and the crystal structures of the elements is considered. Seven basic laws of design are presented and described on a number of examples. The space of design is described with use of the scheme of the Tree of Life divided into ten Spheres of the Worlds which are forming four levels of manifestation: the Design ideas; Realization of Ideas (thinking process); Radiation (including emotions and feelings); Action (implementation), and also division of each of these spheres into sublevels. Possibility of calculation and use of discrete power levels to the description and characteristics of the projected products, and tendencies to replacement of usual options on integrated, hybrid and morphing are shown.