The L/sup 1/-norm of out-of-phase peaks of the aperiodic auto-correlation function of binary sequences

2002 ◽  
Author(s):  
S. Stanczak ◽  
H. Boche
Keyword(s):  
Correlation Function ◽  
Binary Sequences ◽  
Auto Correlation ◽  
Auto Correlation Function

scholarly journals Various Auto-Correlation Functions of m-Bit Random Numbers Generated from Chaotic Binary Sequences

Entropy ◽  
2021 ◽  
Vol 23 (10) ◽  
pp. 1295
Author(s):  
Akio Tsuneda
Keyword(s):  
Correlation Function ◽  
Correlation Functions ◽  
Numerical Experiments ◽  
Binary Sequences ◽  
Random Numbers ◽  
One Dimensional ◽  
Auto Correlation ◽  
Auto Correlation Function ◽  
Nonlinear Maps ◽  
Correlation Properties

This paper discusses the auto-correlation functions of m-bit random numbers obtained from m chaotic binary sequences generated by one-dimensional nonlinear maps. First, we provide the theoretical auto-correlation function of an m-bit sequence obtained by m binary sequences that are assumed to be uncorrelated to each other. The auto-correlation function is expressed by a simple form using the auto-correlation functions of the binary sequences. This implies that the auto-correlation properties of the m-bit sequences can be easily controlled by the auto-correlation functions of the original binary sequences. In numerical experiments using a computer, we generated m-bit random sequences using some chaotic binary sequences with prescribed auto-correlations generated by one-dimensional chaotic maps. The numerical experiments show that the numerical auto-correlation values are almost equal to the corresponding theoretical ones, and we can generate m-bit sequences with a variety of auto-correlation properties. Furthermore, we also show that the distributions of the generated m-bit sequences are uniform if all of the original binary sequences are balanced (i.e., the probability of 1 (or 0) is equal to 1/2) and independent of one another.

scholarly journals New Orthogonal Small Set Kasami Code Sequence

2015 ◽  
Vol 14 (1) ◽  
Author(s):  
I Nyoman Pramaita ◽  
I G.A.G.K. Diafari ◽  
DNKP Negara ◽  
Agus Dharma
Keyword(s):  
Correlation Function ◽  
Cross Correlation ◽  
Code Sequence ◽  
Cross Correlation Function ◽  
Auto Correlation ◽  
M Sequence ◽  
Auto Correlation Function ◽  
Small Set

In this paper, the authors propose the design of a new orthogonal small set Kasami code sequence generated using combination of non-orthogonal m-sequence and small set Kasami code sequence. The authors demonstrate that the proposed code sequence has comparable auto-correlation function (ACF), cross- correlation function (CCF), peak cross-correlation values with that of the existing orthogonal small set Kasami code sequence. Though the proposed code sequence has less code sequence sets than that of the existing orthogonal small set Kasami code sequence, the proposed code sequence possesses one more numbers of members in each code sequence set. The members of the same code set of the proposed code sequence are orthogonal to each other.

scholarly journals Mapping input noise to escape noise in integrate-and-fire neurons: a level-crossing approach

2021 ◽  
Author(s):  
Tilo Schwalger
Keyword(s):  
Correlation Function ◽  
Hazard Rate ◽  
Second Order ◽  
Level Crossing ◽  
Input Noise ◽  
Integrate And Fire ◽  
Auto Correlation ◽  
Auto Correlation Function ◽  
Decoupling Approximation ◽  
Crossing Theory

AbstractNoise in spiking neurons is commonly modeled by a noisy input current or by generating output spikes stochastically with a voltage-dependent hazard rate (“escape noise”). While input noise lends itself to modeling biophysical noise processes, the phenomenological escape noise is mathematically more tractable. Using the level-crossing theory for differentiable Gaussian processes, we derive an approximate mapping between colored input noise and escape noise in leaky integrate-and-fire neurons. This mapping requires the first-passage-time (FPT) density of an overdamped Brownian particle driven by colored noise with respect to an arbitrarily moving boundary. Starting from the Wiener–Rice series for the FPT density, we apply the second-order decoupling approximation of Stratonovich to the case of moving boundaries and derive a simplified hazard-rate representation that is local in time and numerically efficient. This simplification requires the calculation of the non-stationary auto-correlation function of the level-crossing process: For exponentially correlated input noise (Ornstein–Uhlenbeck process), we obtain an exact formula for the zero-lag auto-correlation as a function of noise parameters, mean membrane potential and its speed, as well as an exponential approximation of the full auto-correlation function. The theory well predicts the FPT and interspike interval densities as well as the population activities obtained from simulations with colored input noise and time-dependent stimulus or boundary. The agreement with simulations is strongly enhanced across the sub- and suprathreshold firing regime compared to a first-order decoupling approximation that neglects correlations between level crossings. The second-order approximation also improves upon a previously proposed theory in the subthreshold regime. Depending on a simplicity-accuracy trade-off, all considered approximations represent useful mappings from colored input noise to escape noise, enabling progress in the theory of neuronal population dynamics.

Generalized spot auto-focusing method with a high-definition auto-correlation function in transmission electron microscopy

Microscopy ◽  
2019 ◽  
Vol 68 (5) ◽  
pp. 395-412
Author(s):  
Shigeto Isakozawa ◽  
Misuzu Baba ◽  
Junpei Amano ◽  
Shohei Sakamoto ◽  
Norio Baba
Keyword(s):  
Correlation Function ◽  
Yeast Cell ◽  
Thin Section ◽  
High Definition ◽  
Auto Correlation ◽  
Transmission Electron ◽  
Wide Range ◽  
Auto Correlation Function ◽  
Spot Image ◽  
Auto Focusing

Abstract The spot auto-focusing (AF) method with a unique high-definition auto-correlation function (HD-ACF) proposed in the previous paper is improved and is now applicable to general specimens at a wide range of magnifications. According to the definition where the AF is defocused to obtain the highest resolution, the proposed method achieves the sharpest HD-ACF profile in the AF spot image. The relationship where the sharpest HD-ACF profile gives the highest resolution is theoretically explained, and practical AF examples for different specimens and magnifications are experimentally demonstrated. Specimens include a yeast cell thin section at 10-k magnification, a standard grating replica used as a ruler at 50-k, a crystal lattice of graphitized carbon at 400-k and a 60°-tilted thin section (yeast cell) at 10-k. Different procedures are prepared to actively identify the defocus position that gives the sharpest HD-ACF profile. Every AF result demonstrates the highest-resolution image.

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