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Modulation and Demodulation Circuitry
Published in Mike Golio, Commercial Wireless Circuits and Components Handbook, 2018
If then our modulation process works directly upon ωc = 2πfc, we say we have performed “frequency” modulation. If, instead, we directly vary the phase factor ϕ(t), we say we have performed “phase” modulation. The two kinds of angle modulation are closely related, so that we may do one kind of operation to get the other result, by proper preprocessing of the modulation signal. Specifically, if we put the modulating signal through an integrating circuit before we feed it to a phase modulator, we come out with frequency modulation. This is, in fact, often done. The dual of this operation is possible but is seldom done in practice. Thus, if the modulating signal is fed through a differentiating circuit before it is fed to a frequency modulator, the result will be phase modulation. However, this process offers no advantages to motivate such efforts.
Quantum Spaces of Tribosystems
Published in Dmitry N. Lyubimov, Kirill N. Dolgopolov, L.S. Pinchuk, Quantum Effects in Tribology, 2017
Dmitry N. Lyubimov, Kirill N. Dolgopolov, L.S. Pinchuk
The length of the bra-vector 〈A| or its conjugate ket-vector |A〉is defined as +⟨A|A⟩ $ + \sqrt {\langle A|A\rangle } $ . If a system state is given and it is necessary to introduce the bra or ket-vectors corresponding to this state, only the vector direction is defined; the vector itself is defined only to an arbitrary factor. It can be conveniently chosen so that the vector leng this equal to one. This procedure is called normalization in quantum-mechanics. The state vector is not fully defined even in this case, since it is not prohibited to multiply it by a coefficient equal module one, i.e.by any number exp(iγ) $ {\text{exp }}(i\gamma ) $ with the real exponent γ without changing the vector length. This coefficient is called a phase factor.
Emergence of Superposition Effects
Published in Chandrasekhar Roychoudhuri, Causal Physics, 2018
Here a is real and represents the time-independent maximum excursion amplitude of the E-vector. We are ignoring the constant and arbitrary phase factor since we are analyzing phase-steady signals. It is traditional to present the argument that we use complex representation only because of computational advantages. However, a careful comparison with the real representation will show that there is an embedded mathematical time-averaging process built into the complex representation.
Multi-functional liquid crystal devices based on random binary matrix algorithm
Published in Liquid Crystals, 2023
Tibin Zeng, Kuangdi Xue, Yingjie Zhou, Xiangyu Jiang, Fan Fan, Shuangchun Wen
In the research of the methods and materials applied in light field modulation, liquid crystal (LC) has been widely used in phase manipulation due to its unique birefringence characteristics and high controllability, such as LC vortex Q-plate, LC polarisation grating (PG) and LC geometric phase lens [17–20]. Unlike the surface structured gratings, LC gratings draw more and more attention for their special properties namely electrical tunability [18], total flat grating surface with less scattering [17], ideally continuous phase profile [19], self-assembled three-dimensional LC structures with high diffraction efficiency in broadband and wide-angle [21] and high resolution. The geometric phase device based on LC has the obvious advantages of low cost, electrically switchable ability and broadband spectral range in operation [17–21]. In addition, unlike dynamic phase devices that rely on changes in optical path difference, the principle of geometric phase factors stems from the manipulation of spatial polarisation changes [22]. The geometric phase factor determines the phase of the output light. The continuous phase change and higher fabrication accuracy make LC devices based on the geometric phase principle more efficient in conversion than other spatial light modulators [18,23].
Research on multi-mode multiplexing OAM antenna system based on offset-fed beam bunching paraboloid
Published in Electromagnetics, 2021
Xian-Zheng Zong, Han-Fei Zhang, Zheng-Tian Chen, Hong-Yu Chu, Chao-Guang Lin, Zai-Ping Nie, Jun Hu, Jun-Jie Wu, Zhong-Yu Li
The electromagnetic wave carrying orbital angular momentum is called vortex electromagnetic wave, the wave front of which generally distributes in space spirally. The expression can be obtained by multiplying the one corresponding to plane wave by a phase factor:
Peak-to-Average-Power-Ratio (PAPR) Reduction Methods with Wavelet Transform in MIMO-OFDM
Published in IETE Journal of Research, 2018
Generally, the phase factor selection is limited to a finite element set in order to reduce complexity. If W is defined as the phase factor number, the phase factor set will be defined in the following way: