# How does a Daniell kernel differ from a two sided average?

As far as I can understand, the Daniell kernel, is simply $K(j/M)=\frac{1}{2M+1}1(|j|\leq M)$.

Namely, this is a two sided average. Why do people call this an untruncated kernel and differentiate it from a kernel of the form $K(j/M)=1(|j|\leq M$) when the only thing different is the scaling factor?

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There is no difference other than the scaling, as you say. Sometimes, "Daniell kernel" is used interchangeably with "modified Daniell kernel", which is identical except that end points receive only half of the weight: you might want to check which variety of Daniell kernel is in fact being used.

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