Fourier transform of top hat function

1. What is a top hat function?
2. What is the Fourier transform of Signum function?
3. What is the Fourier transform of Dirac function?
4. Which function Cannot be expanded as Fourier series?

What is a top hat function?

[1] The Top Hat Transform function is a grey-level image analysis tool that allows extracting peaks and valleys in a non-uniform background. This function can be applied onto a grey-level Digital Elevation Model (DEM).

What is the Fourier transform of Signum function?

The signum function does not satisfy the Dirichlet conditions, and therefore, strictly speaking, it does not have a Fourier transform. Fourier transform of signum function can be obtained by taking a limit on G(f) for a to approach to zero. speaking, they do not have Fourier transform.

What is the Fourier transform of Dirac function?

The Fourier transform of a function (for example, a function of time or space) provides a way to analyse the function in terms of its sinusoidal components of different wavelengths. The function itself is a sum of such components. The Dirac delta function is a highly localized function which is zero almost everywhere.

Which function Cannot be expanded as Fourier series?

So, x(t) is a periodic or not periodic. Since function in (b) is non periodic. So does not satisfy Dirichlet conditionand cannot be expanded in Fourier series.