ANALYSIS OF SIDE LOBES OF THE AUTOCORRELATION FUNCTION OF BINARY CODE SEQUENCES WTH LIMITED SIGNAL CONVOLUTION

2020 ◽  
Author(s):  
S. G. Tolmachev ◽  
Keyword(s):  
Autocorrelation Function ◽  
Binary Code

Fast algorithm for calculating autocorrelation function in code synthesis tasks by enumerative technique

2021 ◽  
Vol 1 (1) ◽  
pp. 13-18
Author(s):  
A. V. Korobeinikov
Keyword(s):  
Computational Complexity ◽  
Autocorrelation Function ◽  
Linear Dependence ◽  
Fast Algorithm ◽  
Binary Code ◽  
Code Combination ◽  
Current Code

The fast algorithm for calculating the autocorrelation function (ACF) of a binary code is developed in relation to the problem of synthesizing codes with a given ACF by enumerative technique. The algorithm is applicable for any duration of the N code. The computational complexity of calculating the ACF is 2N multiplication operations and 2N addition operations. The linear dependence of computational complexity on the duration of the N code is noted. To calculate the ACF of the newly created code combination, the previous code, its ACF, and the index of the changed code element are used. The condition of applicability of the algorithm is that the search of code combinations must be performed by changing only one element in the current code combination. An enumerative technique is proposed that allows a complete enumertion of all 2N existing combinations by sequentially changing the code combination of just one element.

scholarly journals Search for binary code sequences with low autocorrelation sidelobes by the evolutionary method

2020 ◽  
pp. 44-53
Author(s):  
Sergey Sharov ◽  
Sergey Tolmachev
Keyword(s):  
Autocorrelation Function ◽  
Binary Code ◽  
Hamming Distance ◽  
Additional Restriction ◽  
Main Peak ◽  
Minimum Level ◽  
Range Resolution ◽  
Radar Systems ◽  
The Difference ◽  
Aperiodic Autocorrelation

Introduction: The parameters chosen for complex coded signals used in active radar systems of aircraft for detecting objects largelydetermines their qualitative characteristics and the possibility of covert operation. An important task in the design of such on-boardsystems is the formation of ensembles of pseudorandom-noise binary code sequences of a fixed length with predefined characteristics.Purpose: Search for PRN binary code sequences of a given length, optimal by the criterion of the minimum level of the sidelobes of theaperiodic autocorrelation function. Results: A procedure of search for binary code sequences with specified parameters based on theevolutionary approach is proposed. The minimum level of positive sidelobes of the autocorrelation function is used as a criterion forthe selection of code sequences. An additional restriction is imposed on the length of a substring of codes of the same character. Thepossibility of forming a representative array of sequences with the best ratio of the main peak of the aperiodic autocorrelation functionto its maximum positive sidelobe is shown on the example of 31-bit code sequences. An algorithm is proposed for generating a PRNseries of signals using the code sequences found. The Hamming distance is used as a measure of the difference between two binary codesequences in the series. The proposed approach is advantageous as compared to the well-known method of generating PRN signals basedon pseudorandom m-sequences. Practical relevance: The results obtained can be used in algorithms of airborne radar systems with ahigh range resolution to detect physical objects on the background of an underlying surface, for example, objects on the water surface.

Log-log scale roughness spectroscopy of surfaces

1993 ◽  
Vol 51 ◽  
pp. 224-225
Author(s):  
P. Fraundorf ◽  
B. Armbruster
Keyword(s):  
Power Spectrum ◽  
Autocorrelation Function ◽  
Power Spectra ◽  
Scanning Force Microscopy ◽  
Scanning Tunneling ◽  
Tunneling Microscopy ◽  
Force Microscopy ◽  
Scanning Force ◽  
Lateral Structure ◽  
Scale Roughness

Optical interferometry, confocal light microscopy, stereopair scanning electron microscopy, scanning tunneling microscopy, and scanning force microscopy, can produce topographic images of surfaces on size scales reaching from centimeters to Angstroms. Second moment (height variance) statistics of surface topography can be very helpful in quantifying “visually suggested” differences from one surface to the next. The two most common methods for displaying this information are the Fourier power spectrum and its direct space transform, the autocorrelation function or interferogram. Unfortunately, for a surface exhibiting lateral structure over several orders of magnitude in size, both the power spectrum and the autocorrelation function will find most of the information they contain pressed into the plot’s origin. This suggests that we plot power in units of LOG(frequency)≡-LOG(period), but rather than add this logarithmic constraint as another element of abstraction to the analysis of power spectra, we further recommend a shift in paradigm.

PENGUCAPAN MAKHRAJ DARI UNIT BUNYI TERKECIL HURUF HIJAIYAH BERDASARKAN FREKUENSI DASAR DAN FREKUENSI FORMANT UNTUK MEDIA PEMBELAJARAN MEMBACA ALQURAN

ALQALAM ◽  
2015 ◽  
Vol 32 (2) ◽  
pp. 284
Author(s):  
Muhammad Subali ◽  
Miftah Andriansyah ◽  
Christanto Sinambela
Keyword(s):  
College Student ◽  
Fundamental Frequency ◽  
Autocorrelation Function ◽  
Adult Male ◽  
Formant Frequency ◽  
Formant Frequencies ◽  
Male Speaker ◽  
Similarities And Differences

This article aims to look at the similarities and differences in the fundamental frequency and formant frequencies using the autocorrelation function and LPCfunction in GUI MATLAB 2012b on sound hijaiyah letters for adult male speaker beginner and expert based on makhraj pronunciation and both of speaker will be analysis on matching distance of the sound use DTW method on cepstrum. Subject for speech beginner makhraj pronunciation are taken from college student of Universitas Gunadarma and SITC aged 22 years old Data of the speech beginner makhraj pronunciation is recorded using MATLAB algorithm on GUI Subject for speech expert makhraj pronunciation are taken from previous research. They are 20-30 years old from the time of taking data. The sound will be extracted to get the value of the fundamental frequency and formant frequency. After getting both frequencies, it will be obtained analysis of the similarities and differences in the fundamental frequency and formant frequencies of speech beginner and expert and it will shows matching distance of both speech. The result is all of speech beginner and expert based on makhraj pronunciation have different values of fundamental frequency and formant frequency. Then the results of the analysis matching distance using method DTW showed that obtained in the range of 28.9746 to 136.4 between speech beginner and expert based on makhraj pronunciation. Keywords: fundamental frequency, formant frequency, hijaiyah letters, makhraj

A program understanding approach for stripped binary code

2009 ◽  
Vol 28 (10) ◽  
pp. 2608-2612
Author(s):  
Juan-ru LI ◽  
Da-wu GU ◽  
Hai-ning LU
Keyword(s):  
Binary Code ◽  
Program Understanding

Spin-Echo Experiment with NMR Spectra only Partially Narrowed by an Insufficiently Fast Motion

2003 ◽  
Vol 68 (7) ◽  
pp. 1193-1205
Author(s):  
Jaromír Jakeš
Keyword(s):  
Time Delay ◽  
Autocorrelation Function ◽  
Nmr Spectra ◽  
Spin Echo ◽  
Slow Motion ◽  
Linear Least Squares ◽  
Least Squares Adjustment ◽  
Fast Motion ◽  
Motional Narrowing ◽  
Gaussian Line

The spin-echo experiment on a spin system with only partial motional narrowing and an exponential field autocorrelation function is considered. The pattern of the intensity decrease in the echo spectra depends on the ratio τ/τc of the time delay τ in the echo experiment to the correlation time τc of the narrowing motion. With the large ratios (fast motion), the decrease is the same as in the case of extreme narrowing; to obtain undistorted T2 values, the ratio should be at least several units in the single-echo experiment and at least few decades in the multiple-echo experiment. With the small ratios (slow motion), the logarithmic decrease depends non-linearly on τ, and the T2 value found by the linear least-squares adjustment is much longer than that obtained from the extreme narrowing approximation. At very small ratios, the multiple echo yields about 3τc/(ωpτ)2 for T2 as compared with 1/(ωp2rc) obtained from the extreme narrowing approximation; ωp2 is the second moment of the Gaussian line being narrowed. The expression for T2 in the multiple spin echo is similar to that previously found for T2e in the solid multiple spin echo. The echo experiment changes the line shape, which at large τ/τc approaches the Lorentzian one. The case of a multiexponential field autocorrelation function is also briefly considered.

Intervention Modeling

2017 ◽  
Author(s):  
Richard McCleary ◽  
David McDowall ◽  
Bradley J. Bartos
Keyword(s):  
Time Series ◽  
Autocorrelation Function ◽  
Moving Average ◽  
Intervention Model ◽  
Noise Component ◽  
Autoregressive Integrated Moving Average ◽  
Noise Function ◽  
Modeling Strategy ◽  
The Impact ◽  
True Structure

The general AutoRegressive Integrated Moving Average (ARIMA) model can be written as the sum of noise and exogenous components. If an exogenous impact is trivially small, the noise component can be identified with the conventional modeling strategy. If the impact is nontrivial or unknown, the sample AutoCorrelation Function (ACF) will be distorted in unknown ways. Although this problem can be solved most simply when the outcome of interest time series is long and well-behaved, these time series are unfortunately uncommon. The preferred alternative requires that the structure of the intervention is known, allowing the noise function to be identified from the residualized time series. Although few substantive theories specify the “true” structure of the intervention, most specify the dichotomous onset and duration of an impact. Chapter 5 describes this strategy for building an ARIMA intervention model and demonstrates its application to example interventions with abrupt and permanent, gradually accruing, gradually decaying, and complex impacts.

Nondiffusive Brownian Motion Studied by Diffusing-Wave Spectroscopy

1989 ◽  
Vol 177 ◽  
Author(s):  
D. J. Pine ◽  
D. A. Weitz ◽  
D. J. Durian ◽  
P. N. Pusey ◽  
R. J. A. Tough
Keyword(s):  
Autocorrelation Function ◽  
Colloidal Particles ◽  
Scattered Light ◽  
Short Time Scale ◽  
Velocity Autocorrelation Function ◽  
Velocity Autocorrelation ◽  
Power Law Decay ◽  
Brownian Particles ◽  
Short Time ◽  
Surrounding Fluid

ABSTRACTOn a short time scale, Brownian particles undergo a transition from initially ballistic trajectories to diffusive motion. Hydrodynamic interactions with the surrounding fluid lead to a complex time dependence of this transition. We directly probe this transition for colloidal particles by measuring the autocorrelation function of multiply scattered light and observe the effects of the slow power-law decay of the velocity autocorrelation function.

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