Apteronotus said:Fourier is so widely used that there are no shortage of resources online. I would start off with Wiki to get a general idea. There are also ample videos on Youtube.
A Fourier series is a mathematical representation of a periodic function as a sum of sinusoidal functions. It is used to analyze and approximate complex periodic functions.
A Fourier transform is a mathematical operation that decomposes a function into its constituent frequencies. It is used to analyze non-periodic functions or signals in the frequency domain.
A Fourier series is used for periodic functions while a Fourier transform is used for non-periodic functions. A Fourier series represents a function as a sum of sinusoidal functions, while a Fourier transform represents a function as a sum of complex exponential functions.
A Fourier integral is an extension of the Fourier transform to continuous functions. It is used to analyze functions that are not limited to a finite interval and cannot be represented by a Fourier series.
Yes, there are many good online resources for learning about Fourier series, transform, and integral. Some popular sources include Khan Academy, MIT OpenCourseWare, and YouTube channels such as 3Blue1Brown and MathTheBeautiful. Additionally, many universities and educational institutions offer free online courses and materials on these topics.