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Multidimensional Modulation
Multidimensional modulation (MD modulation) is modifying or multiplying an MD signal (typically sinusoidal and referred to as the carrier signal) with another signal that carries some information or message. In the frequency domain, the signal is moved from one frequency to another. if then Typically the carrier signal is a sinusoidal signal and in various applications. The figures below illustrate a quick example of a 2-D modulation. The original signal from () is modulated with a sinusoidal signal to get (). The equations () and () are the real and the imaginary components of the modulated signal. Background/Motivation The MD modulation is one of the properties of the Multidimensional Fourier Transform. MD Fourier Transform (FT) Fourier Transform (FT) of multi-dimensional (MD) signal or system is the transform of the MD signal or system that decomposes it into its frequency components. Essentially, it is the frequency response of the MD signal or system, so it de ...
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Original Plot Of MD Signal
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Real Value Plot Of MD Modulated Signal
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Imaginary Value Plot Of MD Modulated Signal
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Absolute Value Plot Of MD Modulated Signal
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Phase Plot Of MD Modulated Signal
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Multidimensional Transform
In mathematical analysis and applications, multidimensional transforms are used to analyze the frequency content of signals in a domain of two or more dimensions. Multidimensional Fourier transform One of the more popular multidimensional transforms is the Fourier transform, which converts a signal from a time/space domain representation to a frequency domain representation.Smith, W. Handbook of Real-Time Fast Fourier Transforms:Algorithms to Product Testing, Wiley_IEEE Press, edition 1, pages 73–80, 1995 The discrete-domain multidimensional Fourier transform (FT) can be computed as follows: : F(w_1,w_2,\dots,w_m) = \sum_^\infty \sum_^\infty \cdots \sum_^\infty f(n_1,n_2,\dots,n_m) e^ where ''F'' stands for the multidimensional Fourier transform, ''m'' stands for multidimensional dimension. Define ''f'' as a multidimensional discrete-domain signal. The inverse multidimensional Fourier transform is given by : f(n_1,n_2,\dots,n_m) = \left(\frac\right ...
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Fourier Transform
A Fourier transform (FT) is a mathematical transform that decomposes functions into frequency components, which are represented by the output of the transform as a function of frequency. Most commonly functions of time or space are transformed, which will output a function depending on temporal frequency or spatial frequency respectively. That process is also called ''analysis''. An example application would be decomposing the waveform of a musical chord into terms of the intensity of its constituent pitches. The term ''Fourier transform'' refers to both the frequency domain representation and the mathematical operation that associates the frequency domain representation to a function of space or time. The Fourier transform of a function is a complex-valued function representing the complex sinusoids that comprise the original function. For each frequency, the magnitude ( absolute value) of the complex value represents the amplitude of a constituent complex sinusoid wi ...
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3D Scanner
3D scanning is the process of analyzing a real-world object or environment to collect data on its shape and possibly its appearance (e.g. color). The collected data can then be used to construct digital 3D models. A 3D scanner can be based on many different technologies, each with its own limitations, advantages and costs. Many limitations in the kind of objects that can be digitised are still present. For example, optical technology may encounter many difficulties with dark, shiny, reflective or transparent objects. For example, industrial computed tomography scanning, structured-light 3D scanners, LiDAR and Time Of Flight 3D Scanners can be used to construct digital 3D models, without destructive testing. Collected 3D data is useful for a wide variety of applications. These devices are used extensively by the entertainment industry in the production of movies and video games, including virtual reality. Other common applications of this technology include augmented reality, ...
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