Mildenhall Aggregate Loss Tools

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Example 1: Basic FFT Computations

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.