Video Lectures
Lecture 1, Part 1 – Who was Jean-Baptiste Joseph Fourier?
Who was the man whose work on modeling heat transfer led to what we now call the Fourier Transform? Where did he come from and how did he come to propose a theory that was so ahead of its time that without it, the technology enabling you to watch this video wouldn’t exist?
Lecture 1, Part 2 – Fourier And Napoleon
As well as his interest in mathematics, Fourier was very politically active. In this lecture, we look at Fourier’s relationship with one of the most famous figures of French history: Napoleon.
Lecture 1, Part 3 – The Fourier Series
Before delving into the maths of the Fourier Transform, we continue with the third of three 5 minute videos on Fourier himself. After his time in Egypt, Fourier returned to France and began work on his theory of heat flow. He presented his theory in a memoir to the Paris Institute in 1807. Contained in this memoir was the beginnings of an idea which was so ahead of its time, that 200 years later it would revolutionize the way we store and communicate digital data. This idea became known as the Fourier Series.
Lecture 2 – What is Sound?
Now we begin our journey into the actual maths of the Fourier Transform. Throughout the course, we’ll be using sound to demonstrate one of the many uses of Fourier’s theory, so in this lecture we look at what sound actually is, how Fourier’s theory applies to sound, and we even get to see a sound wave propagating through the air.
Lecture 3 – Phase
Sine waves have three properties, amplitude, frequency, and phase. In the last lecture, we dealt with amplitude and frequency. In this lecture, we explore the third and final property of a sine wave: Phase.
Lecture 4 – Euler’s Identity
In order to describe the Fourier Transform, we need a language. That language is the language of complex numbers. Complex numbers are a baffling subject but one that it is necessary to master if we are to properly understand how the Fourier Transform works. What is the imaginary number “i” and why it is so useful to us when dealing with the Fourier Transform?
Lecture 5 – Maths with Complex Numbers
The mathematical beauty of ‘i’, the square route of minus 1, is all very well, but what use to us is a number that cannot be calculated? Well in the Fourier Transform, ‘i’ serves a very important purpose indeed. It keeps things separate, and that is exactly what we want from an algorithm that breaks a signal apart into its constituent sine waves. How does ‘i’ keep things separate and how does this help us?
Lecture 6 – Convolution
What is Convolution? What does it have to do with the Fourier Transform and what is my mischievous little 2-year-old son doing hiding my slippers? Bear with me on this one. Did you know that convolution is the mathematical equivalent of looking for your slippers?
