Fourier analysis

The purpose of spectral density estimation is to measure the amplitude of a signal or a time series according to its frequency [3:5]. The objective is to estimate the spectral density by detecting periodicities in the dataset. A scientist can better understand a signal or time series by analyzing its harmonics.

Note

Spectral theory:

Spectral analysis for time series should not be confused with Spectral Theory, a subset of linear algebra that studies Eigen functions on Hilbert and Banach spaces. In fact, harmonic analysis and Fourier analysis are regarded as a subset of spectral theory.

Let us explore the concept behind the discrete Fourier series as well as its benefits as applied to financial markets. Fourier analysis approximates any generic function as the sum of trigonometric functions, sine and cosine.

Note

Complex Fourier transform:

This section focuses on the discrete Fourier series for real value. The generic Fourier transform applies to complex values [3:6].

The decomposition...