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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.
Visualizing the inner product space ℝm×n in a MATLAB-assisted linear algebra classroom
Published in International Journal of Mathematical Education in Science and Technology, 2018
Prelude: This classroom note considers Frobenius inner product – the mapping defined via for real m × n matrices A and B – in a MATLAB-facilitated learning environment. The examples illustrate the defining properties (symmetry, linearity, positive definiteness) of the inner product along with other notions inherent in the inner product space , such as Frobenius norm (length), distance between vectors, angle between vectors, orthogonal projection, Cauchy–Schwarz inequality, triangle inequality, Pythagorean theorem, parallelogram law, orthogonality and orthonormality, orthonormal basis, completeness relation, coordinates relative to an orthonormal basis and Parseval's identity.