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Prove that $textnorm(F) = frac1N textnorm(f)$ DFT

Show that $sum_N-1^k=0 left | F_k right |^2 = frac2N^2 + 3N + 16$ for DFT coefficients $F_k$Versions of the Fourier TransformIs the aliasing formula for DFT a folklore result?Is there a real representation of the fourier transform?Matlab dft-Set the values of kDiscrete Fourier Transform Proofshow that for $phi in C^0(mathbbR^n)$ with $(1+|x|)^N phi(x)$ boundedDFT of a non-continuous time seriesIntegration of $int exp left[-jmathbfw^H(mathbfz-mathbfAx)-j(mathbfz-mathbfAx)^Hmathbfwright]textdmathbfw$Operator norm of Fourier transform operatorShow that $sum_N-1^k=0 left | F_k right |^2 = frac2N^2 + 3N + 16$ for DFT coefficients $F_k$

0

$begingroup$

Any advice is welcome.

Let $f_n, n = 0, 1, ..., N-1$, be given data values (which may be real or complex) and let $F_k, k = 0, 1, ..., N-1$, be the Fourier coefficients of the data. Show that

$$textnorm(F) = frac1N textnorm(f)$$

where the norm of a vector $a = [a_0, ..., a_n-1]$ having complex coefficients is given by

$$textnorm(a) = sum_N-1^k=0 a_kbara_k$$

Where $bara_k$ denotes complex conjugation.

fourier-transform

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edited Mar 21 at 18:45

hegerber

asked Mar 21 at 4:58

hegerberhegerber

11

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Look at the matrix $W_n,k = e^2i pi nk/N$ then $W W^* = ?$
  $endgroup$
  – reuns
  Mar 21 at 18:53
  
  

  
  
  
  

add a comment | 

0

$begingroup$

Any advice is welcome.

Let $f_n, n = 0, 1, ..., N-1$, be given data values (which may be real or complex) and let $F_k, k = 0, 1, ..., N-1$, be the Fourier coefficients of the data. Show that

$$textnorm(F) = frac1N textnorm(f)$$

where the norm of a vector $a = [a_0, ..., a_n-1]$ having complex coefficients is given by

$$textnorm(a) = sum_N-1^k=0 a_kbara_k$$

Where $bara_k$ denotes complex conjugation.

fourier-transform

share|cite|improve this question

edited Mar 21 at 18:45

hegerber

asked Mar 21 at 4:58

hegerberhegerber

11

$endgroup$

• 
  
  
  

  
  

  
  
  
  
  
  

  
  $begingroup$
  Look at the matrix $W_n,k = e^2i pi nk/N$ then $W W^* = ?$
  $endgroup$
  – reuns
  Mar 21 at 18:53
  
  

  
  
  
  

add a comment | 

$begingroup$

Any advice is welcome.

Let $f_n, n = 0, 1, ..., N-1$, be given data values (which may be real or complex) and let $F_k, k = 0, 1, ..., N-1$, be the Fourier coefficients of the data. Show that

$$textnorm(F) = frac1N textnorm(f)$$

where the norm of a vector $a = [a_0, ..., a_n-1]$ having complex coefficients is given by

$$textnorm(a) = sum_N-1^k=0 a_kbara_k$$

Where $bara_k$ denotes complex conjugation.

fourier-transform

share|cite|improve this question

edited Mar 21 at 18:45

hegerber

asked Mar 21 at 4:58

hegerberhegerber

11

$endgroup$

share|cite|improve this question

edited Mar 21 at 18:45

hegerber

asked Mar 21 at 4:58

hegerberhegerber

11

share|cite|improve this question

edited Mar 21 at 18:45

hegerber

asked Mar 21 at 4:58

hegerberhegerber

11

asked Mar 21 at 4:58

hegerberhegerber

11

asked Mar 21 at 4:58

hegerberhegerber

11