Complete Discrete Fourier Transform Toolkit

This is an expansion from my Discrete Fourier Transform Overlay indicator which offers various features that may be useful for traders wishing to apply frequency analysis or integral transform to their trading. For those unfamiliar with the concept, the discrete Fourier transform decomposes wave or wave-like data into functions depending on frequency. This can be helpful in demonstrating or interpreting trends and periodic frequencies in time-series price data, or oscillating indicators.

This toolkit has the following features:

• Fourier bands (deviation cloud): The deviation cloud expresses the uncertainty in the DFT algorithm, as well as the relative change in frequency of the curve.
  
• Fourier supertrend: The supertrend is applied as a product of the DFT algorithm, instead of onto the price data itself. This filters the supertrend from infrequent periodicities. For trading, this means that the supertrend will not be affected by false breakouts or breakdowns. See the image below for an example:
  
  

Future updates may include:

• Projection of the probabilistic uncertainty principle. In a nutshell, the concept can be used to project uncertainties forwards through price data to forecast the path of least resistance, or, the most probable frequency.
  
• Machine learning capabilities. Justin Doherty has done the Pine Script community a great service in introducing kNN algorithms with Lorentzian distance calculations; however, this is only the start of relativistic mechanics that can be applied to time series data. The DFT algorithm essentially filters data into its periodicities; this data can be inserted into a relativistic kNN algorithm - Lorenz or otherwise - to possibly improve accuracy.