Fdtxjr

Strange behaviour of Check

Cauchy Sequence Characterized only By Directly Neighbouring Sequence Members

What did Darwin mean by 'squib' here?

When is phishing education going too far?

What are the performance impacts of 'functional' Rust?

Antler Helmet: Can it work?

Was credit for the black hole image misattributed?

How do we build a confidence interval for the parameter of the exponential distribution?

Unable to start mainnet node docker container

How do you clear the ApexPages.getMessages() collection in a test?

Are my PIs rude or am I just being too sensitive?

What can I do if my MacBook isn’t charging but already ran out?

Is dark matter really a meaningful hypothesis?

How can players take actions together that are impossible otherwise?

Slither Like a Snake

Cold is to Refrigerator as warm is to?

Is there a documented rationale why the House Ways and Means chairman can demand tax info?

How do I keep my slimes from escaping their pens?

What do you call a plan that's an alternative plan in case your initial plan fails?

How to say that you spent the night with someone, you were only sleeping and nothing else?

Direct Experience of Meditation

How does modal jazz use chord progressions?

How to say 'striped' in Latin

How to set letter above or below the symbol?

Integrals involving Dirichlet kernel and sinc function

0

$begingroup$

I am looking to evaluate the following definite integral involving Dirichlet kernel and sinc function with phase.
beginequationI(d) = int_-infty^infty fracsin[N(k^"-k^')]sin(k^"-k^') fracsin(c(k^"-k^'))c(k^"-k^') fracsin(Nk^')sin(k^') fracsin(ck^')ck^' exp(ik^'d+iphi(k^')) rect Big(frack^'k_0Big) dk^' endequation

Seems to be difficult due to Dirichlet kernel. Thank you in advance.

definite-integrals convolution

share|cite|improve this question

edited Mar 28 at 9:25

user16409

asked Mar 25 at 21:02

user16409user16409

85111

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  No, the Dirichlet kernel cancel and with $int_-infty^infty$ instead of $int_0^k_0$ it would have a closed form.
  $endgroup$
  – reuns
  Mar 25 at 22:13
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Kindly explain how they cancel? btw, I corrected for missing constant in the sinc argument.
  $endgroup$
  – user16409
  Mar 25 at 22:52
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  With your $c$ they don't anymore. Why would you want to evaluate $int_0^k_0$ ? With $int_-infty^infty$ it still has a closed form
  $endgroup$
  – reuns
  Mar 25 at 22:54
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  $int_0^k_0$ ? --> I have optical low pass filter that limits spatial frequencies.
  $endgroup$
  – user16409
  Mar 25 at 23:06
  

  
  
  
  

add a comment | 

0

$begingroup$

I am looking to evaluate the following definite integral involving Dirichlet kernel and sinc function with phase.
beginequationI(d) = int_-infty^infty fracsin[N(k^"-k^')]sin(k^"-k^') fracsin(c(k^"-k^'))c(k^"-k^') fracsin(Nk^')sin(k^') fracsin(ck^')ck^' exp(ik^'d+iphi(k^')) rect Big(frack^'k_0Big) dk^' endequation

Seems to be difficult due to Dirichlet kernel. Thank you in advance.

definite-integrals convolution

share|cite|improve this question

edited Mar 28 at 9:25

user16409

asked Mar 25 at 21:02

user16409user16409

85111

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  No, the Dirichlet kernel cancel and with $int_-infty^infty$ instead of $int_0^k_0$ it would have a closed form.
  $endgroup$
  – reuns
  Mar 25 at 22:13
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Kindly explain how they cancel? btw, I corrected for missing constant in the sinc argument.
  $endgroup$
  – user16409
  Mar 25 at 22:52
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  With your $c$ they don't anymore. Why would you want to evaluate $int_0^k_0$ ? With $int_-infty^infty$ it still has a closed form
  $endgroup$
  – reuns
  Mar 25 at 22:54
  
  

  
  
  
  


• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  $int_0^k_0$ ? --> I have optical low pass filter that limits spatial frequencies.
  $endgroup$
  – user16409
  Mar 25 at 23:06
  

  
  
  
  

add a comment | 

$begingroup$

I am looking to evaluate the following definite integral involving Dirichlet kernel and sinc function with phase.
beginequationI(d) = int_-infty^infty fracsin[N(k^"-k^')]sin(k^"-k^') fracsin(c(k^"-k^'))c(k^"-k^') fracsin(Nk^')sin(k^') fracsin(ck^')ck^' exp(ik^'d+iphi(k^')) rect Big(frack^'k_0Big) dk^' endequation

Seems to be difficult due to Dirichlet kernel. Thank you in advance.

definite-integrals convolution

share|cite|improve this question

edited Mar 28 at 9:25

user16409

asked Mar 25 at 21:02

user16409user16409

85111

$endgroup$

share|cite|improve this question

edited Mar 28 at 9:25

user16409

asked Mar 25 at 21:02

user16409user16409

85111

share|cite|improve this question

edited Mar 28 at 9:25

user16409

asked Mar 25 at 21:02

user16409user16409

85111

asked Mar 25 at 21:02

user16409user16409

85111

asked Mar 25 at 21:02

user16409user16409

85111