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Scala: Guide for Data Science Professionals by Patrick R. Nicolas, Arun Manivannan, Pascal Bugnion

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Fourier analysis

The purpose of spectral density estimation is to measure the amplitude of a signal or a time series according to its frequency [3:4]. The spectral density is estimated by detecting periodicities in the dataset. A scientist can better understand a signal or time series by analyzing its harmonics.

Note

The spectral theory

Spectral analysis for time series should not be confused with spectral theory, a subset of linear algebra that studies Eigenfunctions on Hilbert and Banach spaces. Harmonic and Fourier analyses are regarded as a subset of spectral theory.

The fast Fourier transform (FFT) is the most commonly used frequency analysis algorithm [3:5]. Let's explore the concept behind the discrete Fourier series and the Fourier transform ...

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