Fourier Analysis - FFT and DFT
Welcome to "Statistics for Business Students" Textbook

Recently I have done some work related to frequency analysis. As I was ploughing through my problem and researching the web, I realised how poorly this subject is explained. Don't get me wrong. Some resources are extremely valuable and truly educational. However, most of them put a specific spin on the topic, depending whether they were created by and for mathematicians, engineers, statisticians, or any other profession that stumbled upon this topic. More importantly, I discovered that hardly any one of them offers a practical guide on how to actually execute these calculations efficiently.

This prompted me to write a clean, honest and uncomplicated tutorial on FFT and how to calculate DFTs using Excel. The tutorial can be found here, and the spreadsheet that contains all the accompanying calculations is placed here. I used one single time series, the monthly average temperatures shown in degrees C in Sheffield, South Yorkshire between January 1977 and August 2019 (courtesy of: The time series is obviously periodic, which was cool and served well to demonstrate the method.