Ttdfjt

Classify 2-dim p-adic galois representations

Trace in the category of propositional statements

Is it OK to throw pebbles and stones in streams, waterfalls, ponds, etc.?

What is this fluorinated organic substance?

Are all notation equal by derivatives?

What prevents a US state from colonizing a smaller state?

What is the meaning of ゴト in the context of 鮎

Why would Dementors torture a Death Eater if they are loyal to Voldemort?

Tricky riddle from sister

How do I tell my girlfriend she's been buying me books by the wrong author for the last nine months?

What is the meaning of "it" in "as luck would have it"?

Aligning arrays within arrays within another array

Odd PCB Layout for Voltage Regulator

How can solar sailed ships be protected from space debris?

Disk usage confusion: 10G missing on Linux home partition on SSD

Merging two data frames into a new one with unique items marked with 1 or 0

Can I hire several veteran soldiers to accompany me?

How to idiomatically express the idea "if you can cheat without being caught, do it"

Is it theoretically possible to hack printer using scanner tray?

Is this house-rule removing the increased effect of cantrips at higher character levels balanced?

How soon after takeoff can you recline your airplane seat?

Existence of infinite set of positive integers s.t sum of reciprocals is rational and set of primes dividing an element is infinite

What's the idiomatic (or best) way to trim surrounding whitespace from a string?

How far can gerrymandering go?

Who came up with the convolution theorem?

Conditionally convergent seriesWho came up with the laws of conservation of momentum?Was the term “manifold” (or its German equivalent) chosen with the verb “to fold” in mind?F. Schoblik's announced ''ausführliche Darstellung": a lost wrong proof of the Four Color Theorem?Who discovered the Virial Theorem?What is history behind Smith-Volterra-Cantor sets?Who came up with a number of the theoretical plates equation?Earliest Instances of a Slope/Direction Field for a First-Order ODEHow is the word kernel associated with distributions?Who first defined polynomials as sequences?

3

$begingroup$

I am looking for the earliest reference which proposed the convolution theorem which is often utilized in signal processing (i.e., convolution becomes a multiplication in the Fourier domain).

The Earliest Known Uses of the Word of Mathematics websites gives lot of details on the word convolution, but who was the first person to specifically show the above mentioned property- the connection of Fourier transforms with convolution? Thanks.

mathematics reference-request fourier

share|improve this question

asked Jun 24 at 1:03

M. FarooqM. Farooq

1,15244 silver badges1616 bronze badges

$endgroup$

add a comment | 

3

$begingroup$

I am looking for the earliest reference which proposed the convolution theorem which is often utilized in signal processing (i.e., convolution becomes a multiplication in the Fourier domain).

The Earliest Known Uses of the Word of Mathematics websites gives lot of details on the word convolution, but who was the first person to specifically show the above mentioned property- the connection of Fourier transforms with convolution? Thanks.

mathematics reference-request fourier

share|improve this question

asked Jun 24 at 1:03

M. FarooqM. Farooq

1,15244 silver badges1616 bronze badges

$endgroup$

add a comment | 

$begingroup$

I am looking for the earliest reference which proposed the convolution theorem which is often utilized in signal processing (i.e., convolution becomes a multiplication in the Fourier domain).

The Earliest Known Uses of the Word of Mathematics websites gives lot of details on the word convolution, but who was the first person to specifically show the above mentioned property- the connection of Fourier transforms with convolution? Thanks.

mathematics reference-request fourier

share|improve this question

asked Jun 24 at 1:03

M. FarooqM. Farooq

1,15244 silver badges1616 bronze badges

$endgroup$

share|improve this question

asked Jun 24 at 1:03

M. FarooqM. Farooq

1,15244 silver badges1616 bronze badges

share|improve this question

asked Jun 24 at 1:03

M. FarooqM. Farooq

1,15244 silver badges1616 bronze badges

asked Jun 24 at 1:03

M. FarooqM. Farooq

1,15244 silver badges1616 bronze badges

asked Jun 24 at 1:03

M. FarooqM. Farooq

1,15244 silver badges1616 bronze badges

1 Answer
1

active

oldest

votes

4

$begingroup$

Dominguez in History of the Convolution Operation poured through the original sources, and found many of Miller's and Gardner-Barnes's claims and citations to be inaccurate or erroneous. He devotes a separate section to main theorems associated with the convolution, where we read:

"On the other hand, another important theorem related to the CCO is the so-called convolution theorem. In general, the ­theorem establishes that the Laplace transform of the CCO (5) is the product of the Laplace transform of each input function. A similar result holds for (6) when the integral transform is the Fourier transform. In both cases, it is difficult to determine when both theorems appeared for the very first time. However, it can be said that the convolution theorem for (5) appeared in 1899 in Borel’s memoir about divergent series. For the case of (6), the convolution theorem appeared in the 1920 conference by Daniell about Stieltjes–Volterra products. In it, Daniell defined the convolution of any two measures over the real line, and then he applied the two-sided Laplace transform obtaining the corresponding convolution theorem. From it, he implied the result for the Fourier transform".

On the other hand, the rule of multiplying polynomials equivalent to convolving their coefficients (without the terminology or modern notation) appears already in the work of 12th century Islamic mathematician al-Samawal, see Katz, History of mathematics, 9.3.3.

share|improve this answer

answered Jun 24 at 4:09

ConifoldConifold

37.2k11 gold badge6161 silver badges133133 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you, very useful article. Never heard of al-Samawal, will read more about him.
  $endgroup$
  – M. Farooq
  Jun 24 at 4:25
  

  
  
  
  

add a comment | 

Your Answer

StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "587"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);

else
createEditor();

);

function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
autoActivateHeartbeat: false,
convertImagesToLinks: false,
noModals: true,
showLowRepImageUploadWarning: true,
reputationToPostImages: null,
bindNavPrevention: true,
postfix: "",
imageUploader:
brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
allowUrls: true
,
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);

draft saved

draft discarded

Sign up or log in

StackExchange.ready(function ()
StackExchange.helpers.onClickDraftSave('#login-link');
);

Sign up using Google

Sign up using Facebook

Sign up using Email and Password

Post as a guest

Name

Email

Required, but never shown

StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fhsm.stackexchange.com%2fquestions%2f9762%2fwho-came-up-with-the-convolution-theorem%23new-answer', 'question_page');

);

Post as a guest

Name

Email

Required, but never shown

4

$begingroup$

Dominguez in History of the Convolution Operation poured through the original sources, and found many of Miller's and Gardner-Barnes's claims and citations to be inaccurate or erroneous. He devotes a separate section to main theorems associated with the convolution, where we read:

"On the other hand, another important theorem related to the CCO is the so-called convolution theorem. In general, the ­theorem establishes that the Laplace transform of the CCO (5) is the product of the Laplace transform of each input function. A similar result holds for (6) when the integral transform is the Fourier transform. In both cases, it is difficult to determine when both theorems appeared for the very first time. However, it can be said that the convolution theorem for (5) appeared in 1899 in Borel’s memoir about divergent series. For the case of (6), the convolution theorem appeared in the 1920 conference by Daniell about Stieltjes–Volterra products. In it, Daniell defined the convolution of any two measures over the real line, and then he applied the two-sided Laplace transform obtaining the corresponding convolution theorem. From it, he implied the result for the Fourier transform".

On the other hand, the rule of multiplying polynomials equivalent to convolving their coefficients (without the terminology or modern notation) appears already in the work of 12th century Islamic mathematician al-Samawal, see Katz, History of mathematics, 9.3.3.

share|improve this answer

answered Jun 24 at 4:09

ConifoldConifold

37.2k11 gold badge6161 silver badges133133 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you, very useful article. Never heard of al-Samawal, will read more about him.
  $endgroup$
  – M. Farooq
  Jun 24 at 4:25
  

  
  
  
  

add a comment | 

4

$begingroup$

Dominguez in History of the Convolution Operation poured through the original sources, and found many of Miller's and Gardner-Barnes's claims and citations to be inaccurate or erroneous. He devotes a separate section to main theorems associated with the convolution, where we read:

"On the other hand, another important theorem related to the CCO is the so-called convolution theorem. In general, the ­theorem establishes that the Laplace transform of the CCO (5) is the product of the Laplace transform of each input function. A similar result holds for (6) when the integral transform is the Fourier transform. In both cases, it is difficult to determine when both theorems appeared for the very first time. However, it can be said that the convolution theorem for (5) appeared in 1899 in Borel’s memoir about divergent series. For the case of (6), the convolution theorem appeared in the 1920 conference by Daniell about Stieltjes–Volterra products. In it, Daniell defined the convolution of any two measures over the real line, and then he applied the two-sided Laplace transform obtaining the corresponding convolution theorem. From it, he implied the result for the Fourier transform".

On the other hand, the rule of multiplying polynomials equivalent to convolving their coefficients (without the terminology or modern notation) appears already in the work of 12th century Islamic mathematician al-Samawal, see Katz, History of mathematics, 9.3.3.

share|improve this answer

answered Jun 24 at 4:09

ConifoldConifold

37.2k11 gold badge6161 silver badges133133 bronze badges

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Thank you, very useful article. Never heard of al-Samawal, will read more about him.
  $endgroup$
  – M. Farooq
  Jun 24 at 4:25
  

  
  
  
  

add a comment | 

$begingroup$

Dominguez in History of the Convolution Operation poured through the original sources, and found many of Miller's and Gardner-Barnes's claims and citations to be inaccurate or erroneous. He devotes a separate section to main theorems associated with the convolution, where we read:

"On the other hand, another important theorem related to the CCO is the so-called convolution theorem. In general, the ­theorem establishes that the Laplace transform of the CCO (5) is the product of the Laplace transform of each input function. A similar result holds for (6) when the integral transform is the Fourier transform. In both cases, it is difficult to determine when both theorems appeared for the very first time. However, it can be said that the convolution theorem for (5) appeared in 1899 in Borel’s memoir about divergent series. For the case of (6), the convolution theorem appeared in the 1920 conference by Daniell about Stieltjes–Volterra products. In it, Daniell defined the convolution of any two measures over the real line, and then he applied the two-sided Laplace transform obtaining the corresponding convolution theorem. From it, he implied the result for the Fourier transform".

On the other hand, the rule of multiplying polynomials equivalent to convolving their coefficients (without the terminology or modern notation) appears already in the work of 12th century Islamic mathematician al-Samawal, see Katz, History of mathematics, 9.3.3.

share|improve this answer

answered Jun 24 at 4:09

ConifoldConifold

37.2k11 gold badge6161 silver badges133133 bronze badges

$endgroup$

share|improve this answer

answered Jun 24 at 4:09

ConifoldConifold

37.2k11 gold badge6161 silver badges133133 bronze badges

answered Jun 24 at 4:09

ConifoldConifold

37.2k11 gold badge6161 silver badges133133 bronze badges

answered Jun 24 at 4:09

ConifoldConifold

37.2k11 gold badge6161 silver badges133133 bronze badges