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Sinc function. In mathematics, physics and engineering, the sinc function, denoted by sinc (x), has two forms, normalized and unnormalized. [1] In mathematics, the historical unnormalized sinc function is defined for x ≠ 0 by. Alternatively, the unnormalized sinc function is often called the sampling function, indicated as Sa (x). [2]
numpy.org. NumPy (pronounced / ˈnʌmpaɪ / NUM-py) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. [3] The predecessor of NumPy, Numeric, was originally created by Jim Hugunin with ...
In graph theory, the crossing number cr (G) of a graph G is the lowest number of edge crossings of a plane drawing of the graph G. For instance, a graph is planar if and only if its crossing number is zero. Determining the crossing number continues to be of great importance in graph drawing, as user studies have shown that drawing graphs with ...
This implies that + on is the inverse of this isomorphism, and is zero on (). In other words: To find A + b {\displaystyle A^{+}b} for given b {\displaystyle b} in K m {\displaystyle \mathbb {K} ^{m}} , first project b {\displaystyle b} orthogonally onto the range of A {\displaystyle A ...
A variational explanation for the main ingredient of the Canny edge detector, that is, finding the zero crossings of the 2nd derivative along the gradient direction, was shown to be the result of minimizing a Kronrod–Minkowski functional while maximizing the integral over the alignment of the edge with the gradient field (Kimmel and ...
A zero-crossing in a line graph of a waveform representing voltage over time. A zero-crossing is a point where the sign of a mathematical function changes (e.g. from positive to negative), represented by an intercept of the axis (zero value) in the graph of the function. It is a commonly used term in electronics, mathematics, acoustics, and ...
Digamma function. In mathematics, the digamma function is defined as the logarithmic derivative of the gamma function: [1][2][3] It is the first of the polygamma functions. This function is strictly increasing and strictly concave on , [4] and it asymptotically behaves as [5] for complex numbers with large modulus ( ) in the sector with some ...
According to Logan, a signal is uniquely reconstructible from its zero crossings if: The signal x ( t) and its Hilbert transform xt have no zeros in common with each other. The frequency-domain representation of the signal is at most 1 octave long, in other words, it is bandpass - limited between some frequencies B and 2 B.