Concatenation of Legendre symbol sequences

2011 ◽  
Vol 48 (2) ◽  
pp. 193-204
Author(s):  
Katalin Gyarmati
Keyword(s):  
Binary Sequence ◽  
Binary Sequences ◽  
Legendre Symbol ◽  
Pseudorandom Binary Sequence ◽  
Symbol Sequences

In the applications it may occur that our initial pseudorandom binary sequence is not long enough, thus we have to take the concatenation of it with another pseudorandom binary sequences. Here we will consider concatenation of Legendre symbol sequences so that the resulting longer sequence has strong pseudorandom properties.

A finite pseudorandom binary sequence

2001 ◽  
Vol 38 (1-4) ◽  
pp. 377-384 ◽  
Author(s):  
András Sárközy
Keyword(s):  
Binary Sequence ◽  
Binary Sequences ◽  
Pseudorandom Sequence ◽  
Legendre Symbol ◽  
Pseudorandom Sequences ◽  
Pseudorandom Binary Sequence ◽  
Good Sequence

In a series of papers Mauduit and Sárközy studied finite pseudorandom sequences. In particular, in Part I they showed that the Legendre symbol forms an 'ideally good' pseudorandom sequence. In other parts of the series numerous other binary sequences have been tested for pseudorandomness but neither of them proved to be as 'good' as the Legendre symbol. Here another 'very good' sequence is constructed by using the notion of index.

scholarly journals Dietary Nitrate Influence on Oxygen Uptake Response to Pseudorandom Binary Sequence Cycling Protocols

2021 ◽  
Vol 35 (S1) ◽  
Author(s):  
Barry Scheuermann ◽  
Tyler Falor ◽  
Andrew Misko ◽  
Jordan Monnier ◽  
Britton Scheuermann
Keyword(s):  
Oxygen Uptake ◽  
Binary Sequence ◽  
Dietary Nitrate ◽  
Pseudorandom Binary Sequence ◽  
Oxygen Uptake Response

scholarly journals Quasi-Random Graphs, Pseudo-Random Graphs and Pseudorandom Binary Sequences, I. (Quasi-Random Graphs)

2019 ◽  
Vol 14 (2) ◽  
pp. 103-126
Author(s):  
József Borbély ◽  
András Sárközy
Keyword(s):  
Random Graphs ◽  
Adjacency Matrix ◽  
Binary Sequence ◽  
Binary Sequences ◽  
Circulant Graph ◽  
Large Families

AbstractIn the last decades many results have been proved on pseudo-randomness of binary sequences. In this series our goal is to show that using many of these results one can also construct large families of quasi-random, pseudo-random and strongly pseudo-random graphs. Indeed, it will be proved that if the first row of the adjacency matrix of a circulant graph forms a binary sequence which possesses certain pseudorandom properties (and there are many large families of binary sequences known with these properties), then the graph is quasi-random, pseudo-random or strongly pseudo-random, respectively. In particular, here in Part I we will construct large families of quasi-random graphs along these lines. (In Parts II and III we will present and study constructions for pseudo-random and strongly pseudo-random graphs, respectively.)

Signal-to-Clutter Ratio in Pseudo Random Doppler Flowmeter

1986 ◽  
Vol 8 (4) ◽  
pp. 272-284
Author(s):  
Dominique Jean Cathignol
Keyword(s):  
Velocity Measurement ◽  
Signal To Noise Ratio ◽  
Binary Sequence ◽  
Vessel Diameter ◽  
Sine Wave ◽  
Ultrasonic Field ◽  
Pseudorandom Binary Sequence ◽  
Range Cell ◽  
Simultaneous Decrease ◽  
Better Than

In order to increase the signal-to-noise ratio of Doppler velocimeters, several authors have proposed to use the emission of a sine wave phase modulated by a pseudorandom binary sequence with an on/off ratio equal to unity. The velocity measurement of the scatterers located in the range cell volume may be perturbed by all the other reflecting clutter targets which are moving in the ultrasonic field. The ratio between the Doppler signal issuing from the range cell and that from the mobile clutter targets will be defined as the signal-to-mobile clutter ratio (SCR)m. We have evaluated the (SCR)m by computing the ambiguity function of the pseudorandom binary sequence as a function of the vessel diameter, the number of phase states and the normalized particle velocity. The results show: (i) for high velocities, the (SCR)m decreases rapidly. (ii) an increase of the number of states of the code does not entail a proportional improvement in the (SCR)m because of the simultaneous decrease of the range cell;(iii) it is confirmed that pseudorandom flowmeters perform better than pulsed Doppler systems for small, even deep-lying, vessels. However, they do not allow for a precise velocity measurement in the case of vessel diameters larger than three Centimeters.

Kinetics of Oxygen Uptake for Submaximal Exercise in Hyperoxia, Normoxia, and Hypoxia

1995 ◽  
Vol 20 (2) ◽  
pp. 198-210 ◽  
Author(s):  
Richard L. Hughson ◽  
John M. Kowalchuk
Keyword(s):  
Ventilatory Threshold ◽  
Binary Sequence ◽  
Submaximal Exercise ◽  
Work Rate ◽  
Oxygen Deficit ◽  
Gas Mixture ◽  
Pseudorandom Binary Sequence ◽  
Upper Limit ◽  
Kinetics Of ◽  
Hypoxic Gas Mixture

This study evaluated the dynamic response of [Formula: see text] in 6 healthy men at the onset and end of submaximal step changes in work rate during a pseudorandom binary sequence (PRBS) exercise test and during ramp incremental exercise to exhaustion while breathing three different gas mixtures. The fractional concentrations of inspired O2 were 0.14, 0.21, and 0.70 for the hypoxic, normoxic, and hyperoxic tests, respectively. Both maximal [Formula: see text] and work rate was significantly reduced in hypoxic tests compared to normoxic and hyperoxic tests. Maximal work rate was greater in hyperoxia than in normoxia. Work rate at ventilatory threshold was lower in hypoxia than in normoxia and hyperoxia but above the upper limit of exercise for the submaximal tests. Hypoxia significantly slowed the response of [Formula: see text] both at the onset and end of exercise compared to normoxia and hyperoxia. Hypoxia also modified the response to PRBS exercise, and again there was no difference between normoxia and hyperoxia. These data support the concept that [Formula: see text] kinetics can be slowed from the normoxic response by a hypoxic gas mixture. Key words: [Formula: see text]max, ventilatory threshold, oxygen deficit, pseudorandom binary sequence

scholarly journals Some Algebraic Properties of Finite Binary Sequences

2016 ◽  
Vol 65 (1) ◽  
pp. 93-104 ◽  
Author(s):  
Małgorzata Filipczak ◽  
Tomasz Filipczak
Keyword(s):  
Binary Sequence ◽  
Fixed Number ◽  
Binary Sequences ◽  
Algebraic Properties

Abstract We study properties of differences of finite binary sequences with a fixed number of ones, treated as binary numbers from ℤ (2m).We show that any binary sequence consisting of m terms (except of the sequence (1, 0, . . . , 0)) can be presented as a difference of two sequences having exactly n ones, whenever .

Clincal Use of Pseudorandom Binary Sequence White Noise in Assessment of the Human Vestibulo-Ocular System

1978 ◽  
Vol 87 (6) ◽  
pp. 845-852 ◽  
Author(s):  
Conrad Wall ◽  
F. Owen Black ◽  
Dennis P. O'leary
Keyword(s):  
White Noise ◽  
Binary Sequence ◽  
Normal Subjects ◽  
Test Time ◽  
Slow Phase ◽  
Pseudorandom Binary Sequence ◽  
Velocity Response ◽  
Ocular System ◽  
Eye Velocity

White noise rotational stimulation has been used to evaluate the human vestibulo-ocular response for 30 normal subjects over the frequency range from 0.02 to 1.6 Hz and is being extended to characterize response of patients having documented abnormalities. For clinical use, the white noise stimulus has the advantages of shortening the test time by presenting all stimulus frequencies simultaneously, and being well-tolerated by both normal subjects and patients alike. Cross spectral calculations which compare the computer reconstructed slow phase eye velocity response to the pseudorandom acceleration stimulus yield a set of linear and nonlinear estimates of the vestibulo-ocular response. Pilot data indicate that a classification of the disease state can be made using this set of estimates. This classification will be presented and discussed.

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