Learn How To Detect Dominant Cycles With Spectrum Analysis

Using the Fast Fourier Transform and the DFT-Goertzel algorithm to detect cycles in noisy data sets (financial markets)

What you’ll learn
This course explains the key elements of a Fourier-based spectrum analysis.
Understanding the basic computations involved in FFT-based or Goertzel-algorithm-based measurement.
Explaining the core background of FFT in layman terms and concentrate on the important aspects on “how to read a spectrum” plot.
Learn why the Goertzel algorithm outperforms classical Fourier transforms for the purpose of cycles detection in financial markets
Requirements
Basic cycle and/or spectrum analysis knowledge is helpfull, but not mandatory.
Description
There are many issues to consider when analyzing and measuring cycles in financial markets. Unfortunately, it is easy to make incorrect spectral measurements resulting in inaccurate cycle projections either on wrong phase or length gathered from the spectrum plot.This course explains the key elements of a Fourier-based spectrum analysis. We will focus on explaining the core background in layman terms and concentrate on the important aspects on “how to read a spectrum” plot. We will compare different spectrum analysis methods in regards to their performance of detecting exact cycle lengths (“frequency”) components. You will learn why the Goertzel algorithm outperforms classical Fourier transforms for the purpose of cycles detection in financial markets.Understanding the basic computations involved in FFT-based or Goertzel-algorithm-based measurement, knowing how to apply proper scaling, correct non-integer interpolation, converting different units (frequency vs. time) and learning how to read spectrum plots are all critical to the success of cycle analysis and their related projection. Being equipped with this knowledge and using the tools discussed in this application note can bring you more success with your individual cycle analysis application.Compared to an FFT, the Goertzel algorithm is simple and much more efficient for detecting cycles in data series related to financial markets. You will learn and understand why in this course.

Overview

Section 1: Introduction

Lecture 1 Introduction – Example dataset with 3 cycles

Lecture 2 Applying the Fast Fourier Transform “FFT” for cycle detection

Lecture 3 The Fourier index coefficient – time / frequency conversion

Section 2: Improving the Fast-Fourier-Transform

Lecture 4 Improving FFT resolution using “zero padding” (a)

Lecture 5 Improving FFT resolution: Using interpolation (b)

Lecture 6 Improving FFT resolution: Weighted average around cycle peaks (c)

Section 3: The Goertzel algorithm

Lecture 7 The Goertzel algorithm to detect cycles

Lecture 8 Generalized Goerzel algorithm to detect non-integer coefficients

Section 4: Comparison & Impacts FFT vs. Goertzel-DFT

Lecture 9 Results: Comparison FFT vs Goertzel cycle detection & error rates

Lecture 10 Impact: FFT vs generalized Goertzel error rate in projection area

Data-science and financial market analysts interested in applying digital signal processing to analyzing and measuring cycles in financial markets,Experts who want to understand the differences between standard Fourier and Goertzel algorithm (FFT vs. G-DFT)