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Overview of Digital Communications
Published in M.P. Kennedy, R. Rovatti, G. Setti, Chaotic Electronics in Telecommunications, 2018
Géza Kolumbán, Michael Peter Kennedy
High bandwidth efficiency requires a large signal set. The main advantage of using orthonormal basis functions is that a huge signal set can be generated from a small number of basis functions. Typically, a pair of quadrature sinusoidal signals (a cosine and a sine) is used as the set of basis functions. Since quadrature sinusoidal signals can be generated using a simple phase shifter, it is sufficient to know (or recover) only one sinusoidal signal at the receiver.
Matrices and Linear Algebra
Published in William S. Levine, The Control Handbook: Control System Fundamentals, 2017
Let V be an inner product space, a vector space with an inner product and compatible norm. A set of mutually orthogonal vectors is known as an orthogonal set, and a basis consisting of mutually orthogonal vectors is known as an orthogonal basis. An orthogonal basis consisting of vectors whose norms are all one (i.e. consisting of vectors having unit length) is called an orthonormal basis.
Matrices and Linear Algebra
Published in William S. Levine, Control System Fundamentals, 2019
Let V be a vector space with an inner product and compatible norm. A set of mutually orthogonal vectors is known as an orthogonal set, and a basis consisting of mutually orthogonal vectors is known as an orthogonal basis. An orthogonal basis consisting of vectors whose norms are all one (i.e., consisting of vectors having unit length) is called an orthonormal basis.
A new orientation relationship between cementite and austenite and coexistence of pseudo-primary and secondary dislocations in the habit plane
Published in Philosophical Magazine, 2018
A secondary preferred state must be specified as the reference for the evaluation of the secondary misfit for the calculation of secondary dislocations. This secondary preferred state can be represented by CCSL. The construction of CCSL is guided by the periodic pattern in the GMS cluster centred at the origin in Figure 7(a). According to the lattice parameters, the misfit strain within a GMS defined by vectors and , and another GMS defined by vectors and are 1.1 and 2.3% with respect to austenite lattice, respectively. By applying a hypothetical slight strain to the austenite lattice, the match becomes exact in each GMS, which is now a CCSL point. The resultant CCSL is given in Figure 8. The deviation between any pair of lattice points defining a GMS in the GMS cluster centred at the origin defines a misfit displacement vector. The 2D misfit strain field can be determined based on two non-linearly-related pairs of lattice points. The smallest vectors in horizontal and vertical directions in Figure 8 have been selected as the corresponding vectors, as listed in Table 3. The calculation is made using the following orthonormal basis: , . Slightly different lengths in the above corresponding vectors can be read directly in the diagonal elements in matrices and, when corresponding vectors are expressed in the orthonormal basis. Because the column vectors in and are related by the secondary misfit strain, one can obtain the misfit deformation matrix by , which is also given in Table 3.