The FFT butterfly is a graphical method of showing multiplications and additions involving the samples. Standard graph flow notation is used where each circle with entering arrows is an addition of the two values at the end of the arrows multiplied by a constant. The constant is a number which appears beside the arrow, if there is no value then the constant is taken as one. Here's a simple example that multiplies the two inputs and adds them together......

 Using this notation we can construct butterfly networks that, together, perform the FFT. Two examples of Time Decimation Butterflies.

Don't worry about all the math symbols in the diagram, I'll explain them to you....

The first one performs two complex multiplications and 2 complex additions, while the second one performs only one complex multiplications, and two complex additions..

In the above diagram each circle is the sum of it's inputs (addition) and the values which appear next to the arrows are the multiplications.

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