In generalized polynomial chaos expansion, polynomial orthogonal to the distribution of uncertain (random) parameter is used. For example, for normally distributed random variable Hermite polynomial is used and for uniformly distributed parameter Legendre polynomial is used because they are perfectly orthogonal to their respective distribution. My question is: Is it possible to use any periodic function as an orthogonal function? Is there is any periodic function exist that is orthogonal to normally distributed random variable?
I am confused on how a periodic function can be used as orthogonal function. The value of a periodic function repeats after regular interval. So, where is the independence which is the vital concept of orthogonality.
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