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Cone-shape Distribution Function
The cone-shape distribution function, also known as the Zhao–Atlas–Marks time-frequency distribution,Leon Cohen, Time Frequency Analysis: Theory and Applications, Prentice Hall, (1994) (acronymized as the ZAM distribution or ZAMD), is one of the members of Cohen's class distribution function. It was first proposed by Yunxin Zhao, Les E. Atlas, and Robert J. Marks II in 1990. The distribution's name stems from the twin cone shape of the distribution's kernel function on the t, \tau plane. The advantage of the cone kernel function is that it can completely remove the cross-term between two components having the same center frequency. Cross-term results from components with the same time center, however, cannot be completely removed by the cone-shaped kernel. Mathematical definition The definition of the cone-shape distribution function is: :C_x(t, f)=\int_^\int_^A_x(\eta,\tau)\Phi(\eta,\tau)\exp (j2\pi(\eta t-\tau f))\, d\eta\, d\tau, where :A_x(\eta,\tau)=\int_^x(t+\tau ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Robert J
The name Robert is an ancient Germanic given name, from Proto-Germanic "fame" and "bright" (''Hrōþiberhtaz''). Compare Old Dutch ''Robrecht'' and Old High German ''Hrodebert'' (a compound of '' Hruod'' () "fame, glory, honour, praise, renown, godlike" and ''berht'' "bright, light, shining"). It is the second most frequently used given name of ancient Germanic origin.Reaney & Wilson, 1997. ''Dictionary of English Surnames''. Oxford University Press. It is also in use as a surname. Another commonly used form of the name is Rupert. After becoming widely used in Continental Europe, the name entered England in its Old French form ''Robert'', where an Old English cognate form (''Hrēodbēorht'', ''Hrodberht'', ''Hrēodbēorð'', ''Hrœdbœrð'', ''Hrœdberð'', ''Hrōðberχtŕ'') had existed before the Norman Conquest. The feminine version is Roberta. The Italian, Portuguese, and Spanish form is Roberto. Robert is also a common name in many Germanic languages, including En ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cone Shape 1
In geometry, a cone is a three-dimensional figure that tapers smoothly from a flat base (typically a circle) to a point not contained in the base, called the ''apex'' or '' vertex''. A cone is formed by a set of line segments, half-lines, or lines connecting a common point, the apex, to all of the points on a base. In the case of line segments, the cone does not extend beyond the base, while in the case of half-lines, it extends infinitely far. In the case of lines, the cone extends infinitely far in both directions from the apex, in which case it is sometimes called a ''double cone''. Each of the two halves of a double cone split at the apex is called a ''nappe''. Depending on the author, the base may be restricted to a circle, any one-dimensional quadratic form in the plane, any closed one-dimensional figure, or any of the above plus all the enclosed points. If the enclosed points are included in the base, the cone is a solid object; otherwise it is an open surface, a ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MATLAB
MATLAB (an abbreviation of "MATrix LABoratory") is a proprietary multi-paradigm programming language and numeric computing environment developed by MathWorks. MATLAB allows matrix manipulations, plotting of functions and data, implementation of algorithms, creation of user interfaces, and interfacing with programs written in other languages. Although MATLAB is intended primarily for numeric computing, an optional toolbox uses the MuPAD symbolic engine allowing access to symbolic computing abilities. An additional package, Simulink, adds graphical multi-domain simulation and model-based design for dynamic and embedded systems. , MATLAB has more than four million users worldwide. They come from various backgrounds of engineering, science, and economics. , more than 5000 global colleges and universities use MATLAB to support instruction and research. History Origins MATLAB was invented by mathematician and computer programmer Cleve Moler. The idea for MATLAB was base ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
National Instruments
The National Instruments Corporation, doing business as NI, is an America, American multinational corporation, multinational company with international operations. Headquartered in Austin, Texas, Austin, Texas, it is a producer of automated test equipment, semiconductor production, and LabVIEW, virtual instrumentation software. Common applications include data acquisition (DAQ), instrument control, system management, and machine learning and machine vision, vision. Following its acquisition by Emerson Electric, the NI has operated the company’s test and measurement business unit since October 2023. In 2022, the company sold products to more than 35,000 companies worldwide with revenues of USD$1.66 billion. History Founding In the early 1970s, James Truchard, Jeff Kodosky, and Bill Nowlin were employed at the J. J. Pickle Research Campus#Campus, University of Texas at Austin Applied Research Laboratories. While working on a project for the U.S. Navy, they utilized early c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wigner Distribution Function
The Wigner distribution function (WDF) is used in signal processing as a transform in time-frequency analysis. The WDF was first proposed in physics to account for quantum corrections to classical statistical mechanics in 1932 by Eugene Wigner, and it is of importance in quantum mechanics in phase space (see, by way of comparison: '' Wigner quasi-probability distribution'', also called the ''Wigner function'' or the ''Wigner–Ville distribution''). Given the shared algebraic structure between position-momentum and time-frequency conjugate pairs, it also usefully serves in signal processing, as a transform in time-frequency analysis, the subject of this article. Compared to a short-time Fourier transform, such as the Gabor transform, the Wigner distribution function provides the highest possible temporal vs frequency resolution which is mathematically possible within the limitations of the uncertainty principle. The downside is the introduction of large cross terms between eve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ambiguity Function
In pulsed radar and sonar signal processing, an ambiguity function is a two-dimensional function of propagation delay \tau and Doppler frequency f, \chi(\tau,f). It represents the distortion of a returned pulse due to the receiver matched filter (commonly, but not exclusively, used in pulse compression radar) of the return from a moving target. The ambiguity function is defined by the properties of the pulse and of the filter, and not any particular target scenario. Many definitions of the ambiguity function exist; some are restricted to narrowband signals and others are suitable to describe the delay and Doppler relationship of wideband signals. Often the definition of the ambiguity function is given as the magnitude squared of other definitions (WeissWeiss, Lora G. "Wavelets and Wideband Correlation Processing". ''IEEE Signal Processing Magazine'', pp. 13–32, Jan 1994). For a given complex baseband pulse s(t), the narrowband ambiguity function is given by :\chi(\tau,f)=\int_^ ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Short-time Fourier Transform
The short-time Fourier transform (STFT) is a Fourier-related transform used to determine the sinusoidal frequency and phase content of local sections of a signal as it changes over time. In practice, the procedure for computing STFTs is to divide a longer time signal into shorter segments of equal length and then compute the Fourier transform separately on each shorter segment. This reveals the Fourier spectrum on each shorter segment. One then usually plots the changing spectra as a function of time, known as a spectrogram or waterfall plot, such as commonly used in software defined radio (SDR) based spectrum displays. Full bandwidth displays covering the whole range of an SDR commonly use fast Fourier transforms (FFTs) with 2^24 points on desktop computers. Forward STFT Continuous-time STFT Simply, in the continuous-time case, the function to be transformed is multiplied by a window function which is nonzero for only a short period of time. The Fourier transform (a o ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Time–frequency Analysis
In signal processing, time–frequency analysis comprises those techniques that study a signal in both the time and frequency domains simultaneously, using various time–frequency representations. Rather than viewing a 1-dimensional signal (a function, real or complex-valued, whose domain is the real line) and some transform (another function whose domain is the real line, obtained from the original via some transform), time–frequency analysis studies a two-dimensional signal – a function whose domain is the two-dimensional real plane, obtained from the signal via a time–frequency transform. The mathematical motivation for this study is that functions and their transform representation are tightly connected, and they can be understood better by studying them jointly, as a two-dimensional object, rather than separately. A simple example is that the 4-fold periodicity of the Fourier transform – and the fact that two-fold Fourier transform reverses direction – can be interp ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
