# LOG#184. Absement, Fourier and transforms.

In this short post, I am going to relate the relatively unknown notion of absement, the quantity

with some common transforms, in particular, with Fourier series and transforms more naturally.

The Fourier series for a periodic signal is

The coefficients for the real case read

and in the complex case

Key remark: the coefficient in the Fourier transforms is the average absement of .Indeed, the remaining coefficients are also the absement weighted with sinusoidal functions.

Exercise: given the Laplace transform

the discrete Fourier transformation

and the zeta transform

What is the relationship with the absement of the transformation coefficients? Interpret your results.

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