Fourier analysis (basic introduction)

Fourier overview

How to read time series data in time domain and frequency domain

For example, the daily temperature , It is a time domain information ; The horizontal axis is time
And the weekly temperature , It's a “ frequency ” Information on , Frequency domain information ; The horizontal axis is the time interval

Some data are very “ good-looking ”; And some information is hidden in the frequency domain . Through Fourier analysis, time domain data can be transformed into frequency domain data .
（ Spectrum analysis can reveal some results that cannot be seen in the time domain , It brings you all kinds of frequency information , Show you the scattered information clearly ）

Two applications of Fourier transform

1. Spectrum analysis
Some data are very “ good-looking ”; And some information is hidden in the frequency domain . Through Fourier analysis, time domain data can be transformed into frequency domain data .
（ Spectrum analysis can reveal some results that cannot be seen in the time domain , It brings you all kinds of frequency information , Show you the scattered information clearly ）
2. Methods and tools in signal processing

Use convolution theorem to perform some operations in frequency domain
wave filtering 、 Autocorrelation, etc

Considering the amount of data , The calculation of frequency is often simpler and faster than the time-domain calculation of the same effect .

The concept of Fourier transform

There is a lot of noise in the time series
Sine wave + Similarity degree
Use dot product to calculate

Build a sine wave of a specific frequency
Compare similarities
Sine wave and time series （ The signal ） The similarity
The horizontal axis is frequency
The theme ： Construct sine wave
List the similarity of all frequencies
Sinusoidal spectrum or energy