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1. A Convolution is an integral that expresses the amount of overlap of one function as it is shifted over another function


2. For example, in synthesis imaging, the measured dirty map is a Convolution of the "true" CLEAN map with the dirty beam (the Fourier transform of the sampling distribution).

Convolution, Clean

3. Convolution definition is - a form or shape that is folded in curved or tortuous windings

Convolution, Curved

4. How to use Convolution in a sentence.


5. In this video, I'm going to introduce you to the concept of the Convolution, one of the first times a mathematician's actually named something similar to what it's actually doing

Concept, Convolution

6. Like making engineering students squirm? Have them explain Convolution and (if you're barbarous) the Convolution theorem


7. They'll mutter something about sliding windows as they try to escape through one. Convolution is usually introduced with its formal definition:


8. What is Convolution? Convolution is a mathematical operation that expresses a relationship between an input signal, the output signal, and …


9. In probability theory, Convolution is a mathematical operation that allows to derive the distribution of a sum of two random variables from the distributions of the two summands


10. In the case of discrete random variables, the Convolution is obtained by summing a series of products of the probability mass functions (pmfs) of the two variables.

Case, Convolution

11. Welcome to the Convolution Bulletin Board System (BBS)


12. This other method is known as Convolution. Usually the black box (system) used for image processing is an LTI system or linear time invariant system


13. Convolution definition, a rolled up or coiled condition

Convolution, Coiled, Condition

14. Convolution is a widely used technique in signal processing, image processing, and other engineering / science fields


15. In Deep Learning, a kind of model architecture, Convolutional Neural Network (CNN), is named after this technique

Convolutional, Cnn

16. However, Convolution in deep learning is essentially the cross-correlation in signal / image processing.

Convolution, Cross, Correlation

17. Convolution In Lecture 3 we introduced and defined a variety of system properties to which we will make frequent reference throughout the course

Convolution, Course

18. What is Convolution? If you've found yourself asking that question to no avail, this video is for you! Minimum maths, maximum intuition here to really help y


19. Convolution integrals are very useful in the following kinds of problems


20. Convolution Let f(x) and g(x) be continuous real-valued functions forx∈R and assume that f or g is zero outside some bounded set (this assumption can be relaxed a bit)

Convolution, Continuous, Can

21. Define the Convolution (f ∗g)(x):= Z ∞ −∞ f(x−y)g(y)dy (1) One preliminary useful observation is f ∗g …


22. Convolution noun [C usually plural] (TWIST)


23. The second Convolution layer’s filters slide over the (32x32x64) feature map taking a slice of 3 x 3 x 64 at a time


24. The Solution: 1×1 Convolution


25. 1×1 Convolution also called pointwise Convolution behaves like a typical Convolution layer with filter size 1×1

Convolution, Called

26. Convolution is a mathematical way of combining two signals to form a third signal

Convolution, Combining

27. Convolution • g*h is a function of time, and g*h = h*g – The Convolution is one member of a transform pair • The Fourier transform of the Convolution is the product of the two Fourier transforms! – This is the Convolution Theorem g∗h↔G(f)H(f)


28. Convolution is a mathematical operation used to express the relation between input and output of an LTI system


29. Convolution is an important operation in signal and image processing


30. Convolution op-erates on two signals (in 1D) or two images (in 2D): you can think of one as the \input" signal (or image), and the other (called the kernel) as a \ lter" on the input image, pro-ducing an output image (so Convolution takes two images as input and produces a third

Convolution, Can, Called

31. Definition The Convolution of piecewise continuous functions f, g : R → R is the function f ∗g : R → R given by (f ∗g)(t) = Z t 0 f(τ)g(t −τ)dτ

Convolution, Continuous

32. I The definition of Convolution of two functions also holds in


33. Convolution, one of the most important concepts in electrical engineering, can be used to determine the output a system produces for a given input signal

Convolution, Concepts, Can

34. final Convolution result is obtained the Convolution time shifting formula should be applied appropriately


35. In addition, the Convolution continuity property may be used to check the obtained Convolution result, which requires that at the boundaries of adjacent intervals the Convolution remains a continuous function of the parameter .

Convolution, Continuity, Check, Continuous

36. Welcome! The behavior of a linear, continuous-time, time-invariant system with input signal x(t) and output signal y(t) is described by the Convolution integral

Continuous, Convolution

37. Convolution is a useful process because it accurately describes some effects that occur widely in scientific measurements, such as the influence of a frequency filter on an electrical signal or of the spectral bandpass of a spectrometer on the shape of a recorded optical spectrum, which cause the signal to be spread out in time and reduced in

Convolution, Cause

38. Convolution is a formal mathematical operation, just as multiplication, addition, and integration


39. Addition takes two numbers and produces a third number, while Convolution takes two signals and produces a third signal.Convolution is used in the mathematics of many fields, such as probability and statistics.


40. What is Convolution? In purely mathematical terms, Convolution is a function derived from two given functions by integration which expresses how the shape of one is modified by the other.


41. Convolution is a formal mathematical operation, just as multiplication, addition, and integration


42. Addition takes two numbers and produces a third number , while Convolution takes two signals and produces a third signal


43. Convolution is used in the mathematics of many fields, such as probability and statistics.


44. Convolution in Convolutional Neural Networks

Convolution, Convolutional

45. The Convolutional neural network, or CNN for short, is a specialized type of neural network model designed for working with two-dimensional image data, although they can be used with one-dimensional and three-dimensional data.

Convolutional, Cnn, Can

46. Numpy.convolve¶ numpy.convolve (a, v, mode='full') [source] ¶ Returns the discrete, linear Convolution of two one-dimensional sequences

Convolve, Convolution

47. The Convolution operator is often seen in signal processing, where it models the effect of a linear time-invariant system on a signal .In probability theory, the sum of two independent random variables is distributed according to the Convolution of their


48. A circular Convolution uses circular rather than linear representation of the signals being convolved

Circular, Convolution, Convolved

49. The periodic Convolution sum introduced before is a circular Convolution of fixed length—the period of the signals being convolved

Convolution, Circular, Convolved

50. When we use the DFT to compute the response of an LTI system the length of the circular Convolution is given

Compute, Circular, Convolution

51. Convolution is an operation which takes two functions as input, and produces a single function output (much like addition or multiplication of functions)


52. "Convolution Theorem." §15.5 in Mathematical Methods for Physicists, 3rd ed


53. Relationship between Convolution and Fourier transforms • It turns out that convolving two functions is equivalent to multiplying them in the frequency domain – One multiplies the complex numbers representing coefficients at each frequency • In other words, we can perform a Convolution by taking the Fourier transform of both functions,

Convolution, Convolving, Complex, Coefficients, Can

54. In deep learning, a Convolutional neural network (CNN, or ConvNet) is a class of deep neural networks, most commonly applied to analyzing visual imagery

Convolutional, Cnn, Convnet, Class, Commonly

55. They are also known as shift invariant or space invariant artificial neural networks (SIANN), based on the shared-weight architecture of the Convolution kernels that scan the hidden layers and translation invariance characteristics.

Convolution, Characteristics

56. Convolution with multivariate delta functions acts as a point operator: Convolution with a function of bounded support acts as a filter: Generalizations & Extensions (1)


57. Definition The Convolution of piecewise continuous functions f , g : R → R is the function f ∗ g : R → R given by (f ∗ g)(t) = Z t 0 f (τ)g(t − τ) dτ

Convolution, Continuous

58. I The definition of Convolution of two functions also holds in


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CONVOLUTION [ˌkänvəˈlo͞oSHən]

convolution (noun) · convolutions (plural noun) · convolution integral (noun) · convolution integrals (plural noun) · convolutions integral (plural noun)

  • a thing that is complex and difficult to follow.
Synonyms: complexity . intricacy . complication . twist . turn . entanglement . contortion . involvement . tortuousness . convolutedness . involution .
  • a coil or twist, especially one of many.
  • the state of being coiled or twisted, or the process of becoming so.
Synonyms: twist . turn . coil . spiral . twirl . curl . helix . whorl . loop . curlicue . kink . sinuosity . volute . volution . gyrus .
  • a sinuous fold in the surface of the brain.
  • a function derived from two given functions by integration which expresses how the shape of one is modified by the other.
  • a method of determination of the sum of two random variables by integration or summation.