Definition
Spectral analysis can be defined by the following informal formulation : From a finite time/space series data, estimate how the total power is distributed over frequency.
The history of spectral analysis discipline about one century ago, with the works of Schuster, A. [1898][1] on detecting cyclic behavior in time series.
An interesting historical perspective on the development of this field, can be found in Marple Jr, S. L, [1987][2].