|Digital Signal Processing||
Digital algorithm to compute estimate of a power spectral density based on sign signal processing using time-weighting functions
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Pulse random processes spectral density estimation using selected characteristic functions
Keywords: : spectral analysis, pulse random process, characteristic function, statistic characteristics.
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Construction of wavelets with compactly supported functions includes determination of the coefficients hn of the refinement equation:
There are fundamental requirements on scaling φ(x) and wavelet ψ(x) functions lead to the main equations for the coefficients hn of the refinement equation:
The fundamental requirements allow N+1 equations for the coefficients hn, while the total number of coefficients equals 2N. N+1 coincides with 2N only if N=1. If N>1, to generate N-1 equation, the fundamental requirements should be supplemented with additional demands on functions φ(x) and ψ(x). These demands are referred to as secondary. Ingrid Daubechies has suggested secondary demand on wavelet moments :
In paper instead of demands on moments for functions introduced symmetry of the coefficients hn relative to the coefficients hN-1 (or hN) as a secondary demand. This condition links the coefficients of the refinement equation ( hi= h2(n-1)-i).
The paper is proposed a method to improve the accuracy of timing and frequency offset estimation synchronization algorithm Schmidl&Cox. The algorithm Schmidl&Cox is based on the use of two preamble symbols. The first symbol is used for detection the preamble and estimation the fractional frequency offset, the second symbol – to estimate the integer frequency offset. Detection and symbol timing estimation is based on finding the likelihood function. The presence of the second symbol provides the possibility of implementing additional components in the likelihood function. This will reduce the risk of making false decisions in the presence of inter-symbol interference at the stage of symbol timing estimation.
In the proposed method, an additional component of the likelihood function is defined in the frequency domain based on calculations of cross-correlation functions of first and second symbol preamble reference spectrum’s and analyzed block spectrum’s. The resulting likelihood function is based on a weighted application of likelihood function Schmidl & Cox algorithm and additional components.
The research of proposed method effect’s on the accuracy timing and frequency offset estimation for various values of weight coefficient in non-stationary multipath channel is produced. As model of multipath the COST 259 (Typical Urban) was used. The simulation showed that the proposed method for different configurations spatial diversity MIMO can significantly improve the accuracy of timing and frequency offset estimation in non-stationary multipath channel at low signal-to-noise ratios.
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The results of evaluation are as follows. Detection problem requires 16...18 bit word length, the latter being limited by false alarm probability increase. Enumeration problem requires 19...21 bit word length, the latter being limited by arising of enumeration errors. Directions of arrival estimation problem requires 10...12 bit word length, the latter being limited by false directions of arrival arising. Adaptive space filtering problem requires 14...16 bit word length, the latter being limited by signals suppression decrease.
Three problems of the four considered (namely detection, enumeration and adaptive space filtering problems) are solved without explicit forming and inverting covariance matrix of input signals, those steps being substituted by essentially equivalent finding filter that orthogonalizes the rows of input signal matrix. Such a solution has higher numerical stability, i.e. it needs smaller processor word length against explicit forming and inverting covariance matrix, which is demonstrated by direct verification for adaptive space filtering problem as an example.
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Keywords: OCR, optical recognition, handwriting, HMM.
Normalization is necessary not only for the images for recognition but also for the images for model development. Equaliy of number of states in the analyzed image with the model dimension ensures the non-existence of the above-noted problem.
The analysis of 800 graphic images of handwritten words written in twenty different handwritings was performed for the purpose of estimation of normalization parameters.
The analysis of graphic images proved a linear dependence of the mean square deviation of the word length from the average value of its length. Thus, the necessity of the increase of the overlap area of linear dimensions of recognizable words by several word model dimensions. This will ensure that the largest number of word models developed from the handwritten words written in different handwritings is involved in determination of the best model.
The conducted experiment showed a significant effect of normalization. The average increase in the percentage of recognition was 7.7 percent in comparison with the algorithms (neural networks), where skeletonization was not used.
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