This course is an introduction to the Fourier and Laplace Transforms. I introduce this subject both geometrically to give a good intuition using Matlab simulations and an online graphical calculator and also in a more formal mathematical way. The equations are broken down into small elements and an intuitive 3 dimensional graphical method is used in order to build intuition and finally understanding of the mathematics. This 3D intuitive learning approach is also backed up by some solid mathematics. This course has been created in order to give you a core understanding of the methods of mathematical transforms. Some sections are quite advanced and some real thinking is required. Your time and dedication will be rewarded with a deeper understanding of this beautiful subject.

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I can assure you that if you are willing to take the time to comprehend the mathematics then the effort will be rewarded ten fold. For example , Fourier Transform (FT) , Discrete Time Fourier Transform (DTFT) , Discrete Frequency Fourier Transform (DFFT) , Discrete Time and Frequency Fourier Transform (DTFFT) , the Discrete Fourier Transform (DFT), the Fast Fourier Transform (FFT) , discrete versions of the Laplace Transform (Z-transform). How are they all related ?By the end of this course you will understand where they all come from and how they are all related to one another. This is not a course about the practical implementation of transforms. This course is about understanding the core subject at a deeper mathematical level. This course is for those who want to truly understand this subject. If you want a new shiny car just to drive then this is not the course for you. If you want to open up the bonnet and take the engine apart to see how it works then this is definitely the course for you.