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On July 29, 2006, I made significant changes to the (formerly) "Problem statement" section of this article. The derivation that I found there was of great help. I added in a few missing lines of derivation noted by a previous contributor and clarified some points, such as the covariance matrix. I also added another section with an alternate derivation of the matched filter. I believe that it is best to derive the matched filter in the context of the inner conjugate product of the filter and the observed signal, since this requires only the use of vectors, matrices, and their conjugate transposes -- without a need to use transposes and complex conjugation alone. I believe that this significantly reduces the mathematical complexity. I have edited the Lagrangian derivation accordingly. -- Rabbanis 04:46, 30 July 2006 (UTC)
I found the derivations to be very helpful, but I was thrown off by the notation for conjugate transpose. Perhaps the superscript 'H' notation should be explained in the article? In my background, I've never come across the 'H' (I think a dagger is what I saw in my textbooks). Cheers. Unexpect 07:04, 10 February 2007 (UTC)
The definition for y, the conjugate inner product of the filter and the observed signal, is given as a discrete convolution
This looks wrong to me: how can h, *the filter*, be the index parameter to x? Shouldn't it actually be something like
69.121.100.249 22:48, 27 October 2006 (UTC)
I believe that the recent changes to the derivation section on this date are not consistent with the body of the article. Specifically, I refer to the second line of the section stating that is the sum of a signal and i.i.d. noise. My concerns are:
I propose that we revert back to the version prior to 15 Jan 2007. -- Rabbanis 19:08, 16 January 2007 (UTC)
Can someone please clarify what the notation means?
Also, does the in near the end, represents a convolution product? Thanks. -- BlackBaron33 ( talk) 00:13, 9 July 2008 (UTC)
The opening paragraph states: "This is equivalent to convolving the unknown signal with a time-reversed version of the template (cross-correlation)."
I think this is slightly incorrect. Convolution always involves "time-reversal". The sentence should read more like this: "This is equivalent to convolving the unknown signal with the template, or an inner product with the time-reversed template."
Or, am I not understanding this? The "template" mentioned in the introduction is a bit vague. Lavaka ( talk) 19:19, 26 August 2008 (UTC)
I was thinking that - rather than starting the article with 'A matched filter is obtained when....', it would be better to state what a matched filter is. That is.... 'A matched filter is (write defintion here)'. KorgBoy ( talk) 06:17, 24 May 2018 (UTC)
Matched filter بلال الفهد ( talk) 20:21, 11 June 2020 (UTC)
On the one hand there is the convolution in the beginning
on the other hand there is the product
So I'd say one is in the time and one in the frequency domain. That would mean that those are not the same y's and h's etc. Following the wiki article on Laplace transformation one should take care about letters used for functions and arguments, i.e. vs etc. This should be done consistently. Mikuszefski ( talk) 09:44, 27 August 2020 (UTC)
There are three derivations, and none have references. The first two derivations, are, I think for optimal filters that reduce to matched filters under the assumption of white, stationary noise. The third derivation uses different variables and gets a different looking result, but that reduces to the matched filter also. The matched filter itself has a very simple definition that is independent of the nature of the noise (or even that there is noise). The matched filter does not need a derivation. The derivations are not derivations of the matched filter but rather proofs that the matched filter is optimal. That could all be replace with a few sentences paraphrased for a reliable source.
I propose to remove all the derivations. If someone thinks that there should be a derivation, add one derivation and back it with a reliable source. Constant314 ( talk) 22:26, 18 March 2022 (UTC)
This connection looks very interesting, maybe somebody can add more https://nowak.ece.wisc.edu/ece830/ece830_fall11_lecture8.pdf Biggerj1 ( talk) 12:01, 19 February 2024 (UTC)
![]() | This article is rated Start-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||||||||||||
|
On July 29, 2006, I made significant changes to the (formerly) "Problem statement" section of this article. The derivation that I found there was of great help. I added in a few missing lines of derivation noted by a previous contributor and clarified some points, such as the covariance matrix. I also added another section with an alternate derivation of the matched filter. I believe that it is best to derive the matched filter in the context of the inner conjugate product of the filter and the observed signal, since this requires only the use of vectors, matrices, and their conjugate transposes -- without a need to use transposes and complex conjugation alone. I believe that this significantly reduces the mathematical complexity. I have edited the Lagrangian derivation accordingly. -- Rabbanis 04:46, 30 July 2006 (UTC)
I found the derivations to be very helpful, but I was thrown off by the notation for conjugate transpose. Perhaps the superscript 'H' notation should be explained in the article? In my background, I've never come across the 'H' (I think a dagger is what I saw in my textbooks). Cheers. Unexpect 07:04, 10 February 2007 (UTC)
The definition for y, the conjugate inner product of the filter and the observed signal, is given as a discrete convolution
This looks wrong to me: how can h, *the filter*, be the index parameter to x? Shouldn't it actually be something like
69.121.100.249 22:48, 27 October 2006 (UTC)
I believe that the recent changes to the derivation section on this date are not consistent with the body of the article. Specifically, I refer to the second line of the section stating that is the sum of a signal and i.i.d. noise. My concerns are:
I propose that we revert back to the version prior to 15 Jan 2007. -- Rabbanis 19:08, 16 January 2007 (UTC)
Can someone please clarify what the notation means?
Also, does the in near the end, represents a convolution product? Thanks. -- BlackBaron33 ( talk) 00:13, 9 July 2008 (UTC)
The opening paragraph states: "This is equivalent to convolving the unknown signal with a time-reversed version of the template (cross-correlation)."
I think this is slightly incorrect. Convolution always involves "time-reversal". The sentence should read more like this: "This is equivalent to convolving the unknown signal with the template, or an inner product with the time-reversed template."
Or, am I not understanding this? The "template" mentioned in the introduction is a bit vague. Lavaka ( talk) 19:19, 26 August 2008 (UTC)
I was thinking that - rather than starting the article with 'A matched filter is obtained when....', it would be better to state what a matched filter is. That is.... 'A matched filter is (write defintion here)'. KorgBoy ( talk) 06:17, 24 May 2018 (UTC)
Matched filter بلال الفهد ( talk) 20:21, 11 June 2020 (UTC)
On the one hand there is the convolution in the beginning
on the other hand there is the product
So I'd say one is in the time and one in the frequency domain. That would mean that those are not the same y's and h's etc. Following the wiki article on Laplace transformation one should take care about letters used for functions and arguments, i.e. vs etc. This should be done consistently. Mikuszefski ( talk) 09:44, 27 August 2020 (UTC)
There are three derivations, and none have references. The first two derivations, are, I think for optimal filters that reduce to matched filters under the assumption of white, stationary noise. The third derivation uses different variables and gets a different looking result, but that reduces to the matched filter also. The matched filter itself has a very simple definition that is independent of the nature of the noise (or even that there is noise). The matched filter does not need a derivation. The derivations are not derivations of the matched filter but rather proofs that the matched filter is optimal. That could all be replace with a few sentences paraphrased for a reliable source.
I propose to remove all the derivations. If someone thinks that there should be a derivation, add one derivation and back it with a reliable source. Constant314 ( talk) 22:26, 18 March 2022 (UTC)
This connection looks very interesting, maybe somebody can add more https://nowak.ece.wisc.edu/ece830/ece830_fall11_lecture8.pdf Biggerj1 ( talk) 12:01, 19 February 2024 (UTC)