FFT Methods for Transforming, Smoothing, and Correlating Signals

Summary

This reference describes a library of fast Fourier transform routines for processing sampled signals. It covers forward and inverse transforms for complex and real-valued data, a combined transform for two real signals, discrete sine and cosine transforms, smoothing via FFT, and correlation via FFT. The listed functions accept arrays of observations and return transformed values or, for smoothing and correlation, updated signal values.

The notes specify input lengths and array layouts, including power-of-two requirements for several routines. They warn that the routines do not check whether those requirements are met. The document is a function overview rather than a trading method: it gives no market data, trading rules, benchmarks, or performance evidence, and offers little guidance on interpreting transformed frequencies for financial series. Its relevance is as signal-processing infrastructure that a researcher might adapt, with care around array preparation, parameter conventions, and implementation details.

Key ideas

• The library includes forward and inverse FFTs for complex and real signals.
• It can transform two real signals together and also provides discrete sine and cosine transforms.
• FFT-based smoothing and correlation are included as signal-processing operations.
• Several routines require power-of-two input lengths, and the library does not validate this condition.
• The reference provides no financial application or evidence of trading performance.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.