Dgdrxrt

Is it my responsibility to learn a new technology in my own time my employer wants to implement?

Why this way of making earth uninhabitable in Interstellar?

Unclear about dynamic binding

Do I need to write [sic] when a number is less than 10 but isn't written out?

What did we know about the Kessel run before the prequels?

Won the lottery - how do I keep the money?

If Nick Fury and Coulson already knew about aliens (Kree and Skrull) why did they wait until Thor's appearance to start making weapons?

Why did CATV standarize in 75 ohms and everyone else in 50?

Which one is the true statement?

Is French Guiana a (hard) EU border?

Why doesn't UK go for the same deal Japan has with EU to resolve Brexit?

Is there a way to save my career from absolute disaster?

Math-accent symbol over parentheses enclosing accented symbol (amsmath)

How many extra stops do monopods offer for tele photographs?

Why don't programming languages automatically manage the synchronous/asynchronous problem?

How to count occurrences of text in a file?

Find non-case sensitive string in a mixed list of elements?

Does increasing your ability score affect your main stat?

What happened in Rome, when the western empire "fell"?

What steps are necessary to read a Modern SSD in Medieval Europe?

How to scale a tikZ image which is within a figure environment

Would this house-rule that treats advantage as a +1 to the roll instead (and disadvantage as -1) and allows them to stack be balanced?

Is it ever safe to open a suspicious HTML file (e.g. email attachment)?

Newlines in BSD sed vs gsed

Need help with the convolution of two complex functions

2

$begingroup$

Could someone start me off with how to find the convolution of these two functions?

Using the normal equation for convolution seems impossible as a common overlap interval is required for integration. The Fourier convolution theorems also seems inapplicable here.

complex-analysis fourier-analysis convolution

share|cite|improve this question

edited Mar 27 at 18:59

Glorfindel

3,41581830

asked Mar 6 '14 at 15:27

user2802349user2802349

2416

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  $$(f_1ast f_2)(x) = int_mathbbR f_1(x-y)f_2(y),dy$$ is well-defined for these two functions. They both belong to $L^2(mathbbR)$.
  $endgroup$
  – Daniel Fischer
  Mar 6 '14 at 15:29
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I'm still a first year undergrad student, so the whole L^2 functions are new to me. Could you explain the process a little further for me?
  $endgroup$
  – user2802349
  Mar 6 '14 at 16:14
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Sorry, I thought that you knew a little bit of that since you spoke of the Fourier convolution theorems, at least one of which has its natural home in $L^2$. Anyway, for any fixed $x$, the function $h_x(y) = f_1(x-y)f_2(y)$ is defined on all of $mathbbR$ and integrable. Thus the function $xmapsto int_mathbbR h_x(y),dy$ is well-defined (and continuous, but that needs some argument to prove).
  $endgroup$
  – Daniel Fischer
  Mar 6 '14 at 16:21
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Oh I meant the theorems that go with the Fourier Transform and stuff. These: mathworld.wolfram.com/ConvolutionTheorem.html This question is from an assignment from my course. It's way over what we actually learned in class. I've been piecing together my assignment by asking a lot of questions on this place. I'm supposed to find the convolution of these and actually obtain a result. The variable of integration ('y' in your equation) of the convolution equation is the overlap of the two functions, right? If they both have infinite limits, what would that variable be for this instance?
  $endgroup$
  – user2802349
  Mar 6 '14 at 16:33
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I'm not sure what you mean with "overlap". Both functions are defined on all of $mathbbR$ (and square-integrable), so the convolution is given by the formula above. Computing it may be quite hard (depends on what you can use; if you know the residue theorem, it's easy, but I don't think first year undergraduates have that yet).
  $endgroup$
  – Daniel Fischer
  Mar 6 '14 at 16:41
  

  
  
  
  

 | 
show 1 more comment

2

$begingroup$

Could someone start me off with how to find the convolution of these two functions?

Using the normal equation for convolution seems impossible as a common overlap interval is required for integration. The Fourier convolution theorems also seems inapplicable here.

complex-analysis fourier-analysis convolution

share|cite|improve this question

edited Mar 27 at 18:59

Glorfindel

3,41581830

asked Mar 6 '14 at 15:27

user2802349user2802349

2416

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  $$(f_1ast f_2)(x) = int_mathbbR f_1(x-y)f_2(y),dy$$ is well-defined for these two functions. They both belong to $L^2(mathbbR)$.
  $endgroup$
  – Daniel Fischer
  Mar 6 '14 at 15:29
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I'm still a first year undergrad student, so the whole L^2 functions are new to me. Could you explain the process a little further for me?
  $endgroup$
  – user2802349
  Mar 6 '14 at 16:14
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Sorry, I thought that you knew a little bit of that since you spoke of the Fourier convolution theorems, at least one of which has its natural home in $L^2$. Anyway, for any fixed $x$, the function $h_x(y) = f_1(x-y)f_2(y)$ is defined on all of $mathbbR$ and integrable. Thus the function $xmapsto int_mathbbR h_x(y),dy$ is well-defined (and continuous, but that needs some argument to prove).
  $endgroup$
  – Daniel Fischer
  Mar 6 '14 at 16:21
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Oh I meant the theorems that go with the Fourier Transform and stuff. These: mathworld.wolfram.com/ConvolutionTheorem.html This question is from an assignment from my course. It's way over what we actually learned in class. I've been piecing together my assignment by asking a lot of questions on this place. I'm supposed to find the convolution of these and actually obtain a result. The variable of integration ('y' in your equation) of the convolution equation is the overlap of the two functions, right? If they both have infinite limits, what would that variable be for this instance?
  $endgroup$
  – user2802349
  Mar 6 '14 at 16:33
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  I'm not sure what you mean with "overlap". Both functions are defined on all of $mathbbR$ (and square-integrable), so the convolution is given by the formula above. Computing it may be quite hard (depends on what you can use; if you know the residue theorem, it's easy, but I don't think first year undergraduates have that yet).
  $endgroup$
  – Daniel Fischer
  Mar 6 '14 at 16:41
  

  
  
  
  

 | 
show 1 more comment

$begingroup$

Could someone start me off with how to find the convolution of these two functions?

Using the normal equation for convolution seems impossible as a common overlap interval is required for integration. The Fourier convolution theorems also seems inapplicable here.

complex-analysis fourier-analysis convolution

share|cite|improve this question

edited Mar 27 at 18:59

Glorfindel

3,41581830

asked Mar 6 '14 at 15:27

user2802349user2802349

2416

$endgroup$

share|cite|improve this question

edited Mar 27 at 18:59

Glorfindel

3,41581830

asked Mar 6 '14 at 15:27

user2802349user2802349

2416

share|cite|improve this question

edited Mar 27 at 18:59

Glorfindel

3,41581830

asked Mar 6 '14 at 15:27

user2802349user2802349

2416

edited Mar 27 at 18:59

Glorfindel

3,41581830

edited Mar 27 at 18:59

Glorfindel

3,41581830

asked Mar 6 '14 at 15:27

user2802349user2802349

2416

asked Mar 6 '14 at 15:27

user2802349user2802349

2416