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#ActualCornstalks

Posted 08 January 2013 - 10:06 PM

For the Discrete-Fourier Transform

 

You have the following variables/values:

  • Xk: An output of the DFT
  • xn: Input values for the DFT
  • N: The number of complex numbers in x = x0, ... , xN-1  and X = X0, ... , XN-1
  • n: A summation variable, as denoted by the summation
  • e: The mathematical constant, approximately equal to 2.71828 (sometimes called Euler's number, but don't confuse it with Euler's constant γ!)
  • i: The imaginary unit
  • π: Pi
  • k: The "index" of X for the current value being computed

 

To take e to an imaginary power (eix), you use Euler's formula (eix = cosx + isinx)

 

I hope you're familiar with imaginary numbers, as they're the foundation for the DFT.

 

The FFT is a way of computing the DFT. That is, it's just an algorithm for computing the DFT in O(NlogN) time (computing the DFT by dumbly following the above equation requires O(N2) complexity).


#4Cornstalks

Posted 08 January 2013 - 10:01 PM

For the Discrete-Fourier Transform

 

You have the following variables/values:

  • Xk: An output of the DFT
  • xn: Input values for the DFT
  • N: The number of complex numbers in x = x0, ... , xN-1  and X = X0, ... , XN-1
  • n: A summation variable, as denoted by the summation
  • e: The mathematical constant, approximately equal to 2.71828 (sometimes called Euler's number, but don't confuse it with Euler's constant γ!)
  • i: The imaginary unit
  • π: Pi
  • k: The "index" of X for the current value being computed

 

To take e to a imaginary power (eix), you use Euler's formula.


#3Cornstalks

Posted 08 January 2013 - 09:46 PM

For the Discrete-Fourier Transform

 

You have the following variables/values:

  • Xk: An output of the DFT
  • N: The number of complex numbers in x = x0, ... , xN-1  and X = X0, ... , XN-1
  • n: A summation variable, as denoted by the summation
  • e: The mathematical constant, approximately equal to 2.71828 (sometimes called Euler's number, but don't confuse it with Euler's constant γ!)
  • i: The imaginary unit
  • π: Pi
  • k: The "index" of X for the current value being computed

 

To take e to a imaginary power (eix), you use Euler's formula.


#2Cornstalks

Posted 08 January 2013 - 09:42 PM

For the Discrete-Fourier Transform

 

You have the following variables/values:

  • Xk: An output of the DFT
  • N: The number of complex numbers in the x = x0, ... , xN-1  and X = X0, ... , XN-1
  • n: A summation variable, as denoted by the summation
  • e: The mathematical constant, approximately equal to 2.71828 (sometimes called Euler's number, but don't confuse it with Euler's constant γ!)
  • i: The imaginary unit
  • π: Pi
  • k: The "index" of X for the current value being computed

 

To take e to a imaginary power, you use Euler's formula.

 

Note: Wikipedia is down right now, so I can't link of any of its decent articles on anything.


#1Cornstalks

Posted 08 January 2013 - 09:40 PM

For the Discrete-Fourier Transform

 

You have the following variables/values:

  • Xk: An output of the DFT
  • N: The number of complex numbers in the set x and the set X
  • n: A summation variable, as denoted by the summation
  • e: The mathematical constant, approximately equal to 2.71828 (sometimes called Euler's number, but don't confuse it with Euler's constant γ)
  • i: The imaginary unit
  • π: Pi
  • k: The "index" of X for the current value being computed

 

To take e to a imaginary power, you use Euler's formula.

 

Note: Wikipedia is down right now, so I can't link of any of its decent articles on anything.


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