Mildenhall Aggregate
Loss Tools
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Example 1: Basic FFT Computations
0 1 0 0 0 0 0 0
Click FFT or IFFT to get Results...
Notes
Input a vector in the text box as a series of numbers separated by spaces, carriage returns, or commas.
Input distributions are interpreted as P(X=0), P(X=1), ...
Input distribution are padded with zeros to a length which is a power of two.
Buttons on the right give three example distributions. Select and click FFT, or input your own distribution.
Paste FFT button pastes the last FFT into the distribution box. Click IFFT to compute inverse transform. You must only input the top half of the FFT.
The FFT is symmetric: the bottom half is the complex conjugate of the top half.
The first element of the FFT is the sum of the input elements, or 1.0 for a probability distribution.
The middle element of the FFT is the alternating sum of the input elements. This is zero for a symmetric distribution.
References to Wang
Sections 2.1 and 2.2.