Fourier Transform Equation Explained ("Best explanation of the Fourier Transform on all of YouTube")

Signal waveforms are used to visualise and explain the equation for the Fourier Transform. Something I should have been more clear about in the video, is that the equation I wrote is the inverse FT, not the FT. The reason I did this is that I like to start by thinking about the time domain signal x(t) (ie. the actual signal that we observe in the real world), because time is one of the main dimensions that we observe/experience, and we are familiar with signals in this domain. I wrote the equation for the time domain signal in terms of the frequency components (which is actually the Inverse Fourier Transform equation). Once you see the signal from this perspective (ie. as being made up of a sum of individual single-frequency waveforms), then you will understand that there are two ways of viewing the same signal (ie. time-domain and frequency-domain), and that they are related by the Fourier Transform and the Inverse Fourier Transform. That's the important point. Another point to note is that I have used "j" for the complex variable, instead of "i" (which is more commonly used). This is because I am an electrical engineer, and we use "i" for electrical current, so we use "j" for the complex variable to avoid confusing ourselves (... except then of course it can be confusing for physicists and mathematicians! ... sorry about that, but it is just the way it is.) If you would like to support me to make these videos, you can join the Channel Membership, by hitting the "Join" button below the video, and making a contribution to support the cost of a coffee a month. It would be very much appreciated. Or by clicking here: @iain_explains Check out my search for signals in everyday life, by following my social media feeds: Facebook: https://www.facebook.com/profile.php?... Instagram: Instagram: iainexplains Website: http://www.iaincollings.com Related videos: (see http://www.iaincollings.com) • Visualising the Fourier Transform Visualising the Fourier Transform • What is the Fourier Transform? What is the Fourier Transform? ("Brilliant... • What is the Fourier Transform used for? What is the Fourier Transform used for? • Fourier Transform and Inverse Fourier Transform: What's the difference? Fourier Transform and Inverse Fourier Tran... • Is Phase important in the Fourier Transform? Is Phase important in the Fourier Transform? • Fourier Transform of Cosine Function: Fourier Transform of Cos • Fourier Transform of Cosine with Phase Shift: Fourier Transform of Cos with Phase Shift • Fourier Transform of a Sum of Delta Functions: Fourier Transform of a Sum of Delta Functions • Typical Exam Question on Fourier Transform Properties Typical Exam Question on Fourier Transform... • 2D Fourier Transform Explained with Examples 2D Fourier Transform Explained with Examples • What is Negative Frequency?: What is Negative Frequency? • Laplace Transform Equation Explained Laplace Transform Equation Explained • Laplace Transform Region of Convergence Explained Laplace Transform Region of Convergence Ex... • How are the Fourier Series, Fourier Transform, DTFT, DFT, FFT, LT and ZT Related? How are the Fourier Series, Fourier Transf... For a full list of Videos and accompanying Summary Sheets, see the associated website: http://www.iaincollings.com .