iQsFFT

Library "iQsFFT"
TODO: add library description here
2. Summary

A high-performance mathematical library designed to bring advanced spectral analysis and signal processing to the Pine Script ecosystem. This tool allows traders and developers to decompose price action into its underlying cyclical components, helping to distinguish market noise from dominant periodic trends.

3. How It Works

The methodology behind this library is based on digital signal processing (DSP) principles, specifically focusing on frequency domain transformation. Instead of looking at price as a simple time-series, this script translates price data into a frequency spectrum to identify the "DNA" of market movement.

Spectral Decomposition: The algorithm utilizes a complex mathematical transform to break down price movements into various frequencies. This allows the user to see which cycles (short-term vs. long-term) are currently influencing the market most heavily.

Signal Reconstruction: By analyzing the real and imaginary components of price data, the library can assist in filtering out high-frequency noise while retaining the core directional "harmonics" of the asset.

Power Spectrum Analysis: The tool calculates the "energy" behind specific price cycles. This helps in identifying whether a recent price move is a significant structural shift or merely a low-energy fluctuation.

4. Key Features

Dual-Direction Transformation: Supports both forward analysis (time-to-frequency) and inverse reconstruction (frequency-to-time).

Advanced Noise Filtering: Conceptually designed to separate dominant market cycles from random volatility.

Power Density Estimation: Quantifies the strength of specific frequencies to identify market resonance.

Optimized Computation: Built using efficient array-handling logic to manage complex calculations within the TradingView environment.

5. How to Use

As this is a library, it is intended to be integrated into other indicators or strategies.

Step 1: Import the library into your script using the import statement.

Step 2: Prepare your input data (real and imaginary arrays) ensuring the sample size is a power of 2 (e.g., 64, 128, 256) for optimal processing.

Step 3: Call the transformation functions to extract the frequency components of your chosen asset.

Step 4: Utilize the power spectrum output to identify which cycles are currently "dominant" and use them to forecast potential turning points.

6. Settings & Configuration

Transform Direction: Choose between Forward (analysis) or Inverse (reconstruction) modes.

Data Arrays: Input fields for the real and imaginary price components.

Input Size: Configuration for the sample window (requires power-of-two lengths for mathematical validity).