Timeline for Why a Convolution Matrix Is Called a Kernel?
Current License: CC BY-SA 4.0
11 events
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| May 14, 2020 at 18:41 | comment | added | DSP_CS | @Fat32 Then can we also called a correlation matrix as kernel?? | |
| Dec 31, 2019 at 22:52 | history | edited | Fat32 | CC BY-SA 4.0 |
deleted 19 characters in body
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| Dec 31, 2019 at 22:43 | history | edited | Fat32 | CC BY-SA 4.0 |
completely discarded the continuous-time case, and significantly reorganised the discrete-time case.
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| Sep 8, 2017 at 14:48 | vote | accept | bruin | ||
| Sep 8, 2017 at 14:46 | comment | added | bruin | Later today I also took a look of Integral Transform on wikipedia, although I am not able digest most of details at the moment, I am a bit more convinced (or tend to think of) that the term "kernel" in convolution may have some connection with integral transformations in general, as you explained :) | |
| Sep 8, 2017 at 10:34 | comment | added | Fat32 | @bruin You're welcome. Sometimes people forget about the difference... | |
| Sep 8, 2017 at 9:01 | comment | added | bruin | Also thanks for pointing out that "Laplace kernel $e^{st}$ does not consitutde an orthogonal basis", which I was not aware of... | |
| Sep 8, 2017 at 8:53 | comment | added | bruin | Ok, thanks... I guess "A transform in general maps a function into another function by the kernel. Nevertheless the concept of a kernel is a general one and is not bound to any special transform or operator in general" addressed my original question directly. As the kernel concept discussed here is in its very general sense, now I tend to agree with what Marcus commented, that "I don't think there's a strict mathematical connection here". Thanks again. | |
| Sep 8, 2017 at 8:30 | comment | added | Fat32 | a kernel has nothing to do with the base vectors of an orthogonal / orthonormal basis. What you mention is an inner product of a given function with memebers of the basis so as to find the coefficients of decomposition of the signal into its base vectors. A transform in general maps a function into another function by the kernel. Nevertheless the concept of a kernel is a general one and is not bound to any special transform or operator in general. Finally, the Laplace kernel $e^{st}$ does not consitutde an orthogonal basis for example. | |
| Sep 8, 2017 at 7:38 | comment | added | bruin | Thanks for your reply, Fat32. Yes I was refering to convolution matrix in image processing..AFAIK, in the general integral transformation scenarios as you mentioned (FT or LT), what you called a "kernel" is known as an othorgonal basis, that the transformation projects/correlates the original function to the new basis, and there is no need to "flip" the basis, as it would required for kernels in convolution; In vector space, the kernel (of a linear transformation) is its null space, while the transformation is usually represented as a matrix which is called its skeleton... | |
| Sep 7, 2017 at 11:11 | history | answered | Fat32 | CC BY-SA 3.0 |