 Our world is full of noise. Millions of signals fly to and fro every moment of every day. Radio signals, sound signals, light. How is it that we are able to make sense of all this noise? How is it that our eyes and ears can actually understand the world around them? We understand the world around us by analyzing the signals it sends us, and comparing them to known signals that we have seen or heard before. For example, if we see a crowd of people, we know that that crowd is made up of lots of individual people because we know what a person looks like. Two arms, two legs, two eyes and nose and mouth. We recognize that the crowd is simply the same pattern repeated over and over again. What is more, we can sometimes even pick out individual faces within the crowd if we have seen that face before and remember what it looks like. This is the basis of signal analysis, finding and isolating known patterns from a sea of information. Computers are very good at this, and use exactly the same method to analyze streams of data. One of the most prolific tools they use to do this is called the Fourier Transform. The Fourier Transform is everywhere. Few are the days in your life where you won't pick up a piece of technology that implements it to provide you with pictures, videos, music, a phone call, and all manner of everyday applications. However, it's very ubiquity, means that we take the Fourier Transform very much for granted, and fewer other people actually really understand how it leaves its magic. Even those who have heard of it and make conscious use of it often don't know how it actually works. One of the reasons for this may be that on the face of it, the maths can seem a little complicated. This was my initial view when I first met the Fourier Transform on my Electronics Engineering course at university. My Electrismist have thought that having actually managed to get into university and into an engineering school, I must be pretty good at maths. However, what they didn't know was that mathematics is a subject that I have always found the hardest. I think the problem was not that I was incapable of understanding it, rather it had always been explained to me in the wrong way. I crave visual explanations, which is why I was always very good at trigonometry at school. I could actually draw the shapes. However, as things became more abstract, as so often happens in mathematics, no drawings were forthcoming. The amount of Greek would begin to outweigh the amount of English on the lecturer's blackboard, my eyes would glaze over, and understanding would elude me. There must be a way I thought of showing these concepts visually, some analogy that doesn't require pages and pages of Greek letters to explain. Well, after years of actually using the Fourier Transform in my professional life, and my repeated attempts at trying to understand how it works, I think I may have come up with the answer. This is what I would like to share with you in this course. Unfortunately, I cannot promise not to use any maths at all in the course. At the end of the day, the Fourier Transform is a mathematical formula, but every equation will be illustrated by diagrams and animations to explain and show what the maths is doing. By the time we've finished, not only will you know about windowing and how the discrete and fast Fourier Transforms work, but this, rather strange looking equation, the Fourier Transform equation, is actually going to make sense.