Fourier Analysis is a mathematical technique used to analyze complex waveforms. It can identify cycles or patterns in time series data, simplify complex or noisy data, and detect patterns in waveforms. Fourier analysis is important for understanding and interpreting the behavior of waves, and it has applications in many fields such as communications, engineering, and algorithmic trading to try and predict the direction of the stock market and medicine. Through Fourier analysis, researchers are able to quantify the properties of waves as well as predict future trends.
The benefits of using Fourier analysis and synthesis include the ability to decompose complex time series data into simpler trigonometric components, which can help identify true patterns or trends that are hidden by noise and confounding factors. Additionally, it can be used to detect spurious trends or cycles in data, as well as provide an insight into the direction that data will take in the future. While research has found that it is not particularly useful in stock trading, Fourier analysis is still a powerful technique for understanding and interpreting complex data sets.