For example, the arctangent function used above can be expanded as

Note that all even-order terms are zero. This is always the case for

The clipping nonlinearity in Eq. (6.17) is not so amenable to a series expansion. In fact, it is its own series expansion! Since it is not differentiable at , it must be represented as three separate series over the intervals , , and , and the result obtained over these intervals is precisely the definition of in Eq. (6.17).

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University