For the Discrete-Fourier Transform

You have the following variables/values:

• X_k: An output of the DFT
• x_n: Input values for the DFT
• N: The number of complex numbers in x = x₀, ... , x_N-1  and X = X₀, ... , X_N-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 (e^ix), you use Euler's formula (e^ix = 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).

For the Discrete-Fourier Transform

You have the following variables/values:

• X_k: An output of the DFT
• x_n: Input values for the DFT
• N: The number of complex numbers in x = x₀, ... , x_N-1  and X = X₀, ... , X_N-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 (e^ix), you use Euler's formula.

For the Discrete-Fourier Transform

You have the following variables/values:

• X_k: An output of the DFT
• N: The number of complex numbers in x = x₀, ... , x_N-1  and X = X₀, ... , X_N-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 (e^ix), you use Euler's formula.

For the Discrete-Fourier Transform

You have the following variables/values:

• X_k: An output of the DFT
• N: The number of complex numbers in the x = x₀, ... , x_N-1  and X = X₀, ... , X_N-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.

For the Discrete-Fourier Transform

You have the following variables/values:

• X_k: 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.