The convolution product is widely used in many fields, such as signal processing, numerical analysis and so on; however, the convolution theorem in the domain of the windowed metaplectic transformation (WFMT) ha
Arfken, G. "Convolution Theorem." §15.5 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 810-814, 1985.Bracewell, R. "Convolution Theorem." The Fourier Transform and Its Applications, 3rd ed. New York: McGraw-Hill, pp. 108-112, 1999....
However, although the DCT is closely related to the DFT, the multiplication-convolution theorem for the DCT was formulated much after the corresponding relationship for the DFT. In fact, despite the several attempts to establish this relation [31], a complete and more consistent formalization was ...
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A convolution operator is proposed in the WFMT domain, which makes the convolution theorem in the WFMT domain have the same concise form as that in the traditional Fourier transform domain.In this way, we can transform the convolution in the time domain into the product in the metaplectic ...
In math terms, "Convolution in the time domain is multiplication in the frequency (Fourier) domain." Mathematically, this is written: or wheref(x)andg(x)are functions to convolve, with transformsF(s)andG(s). We canprove this theoremwith advanced calculus, that uses theorems I don't quit...
One of the main properties of the convolution operation in signal processing is that it can be implemented either in the original domain (e.g., time) or in the transformed domain (e.g., frequency) via pointwise multiplications. Indeed, the convolution theorem establishes the equivalence, under...
In: Advanced technologies for communications (ATC), Ha Noi, Vietnam, Oct 2016 Google Scholar Podlozhnyuk V (2007) FFT-based 2D convolution Google Scholar WikipediA. https://en.wikipedia.org/wiki/Convolution_theorem Mallat S (2012) Group invariant scattering. Comm Pure Appl Math 65(10):...
In this article, several versatile electromagnetic (EM) waves are presented with predefined shapes and directions based on the holography and convolution theorem. Inspiring the holography theory, a reflective interferogram is characterized by interfering
In the discrete case, the difference operator D f(n) = f(n + 1) − f(n) satisfies an analogous relationship: [Math Processing Error] Convolution theorem The convolution theorem states that [Math Processing Error] where \mathcal{F}\{f\}\, denotes the Fourier transform of f, and k ...