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.

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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? ("Bril...  
• 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...  
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• Fourier Transform of Cosine Function:    • Fourier Transform of Cos  
• Fourier Transform of Cosine with Phase Shift:    • Fourier Transform of Cos with Phase S...  
• Fourier Transform of a Sum of Delta Functions:    • Fourier Transform of a Sum of Delta F...  
• Typical Exam Question on Fourier Transform Properties    • Typical Exam Question on Fourier Tran...  
• 2D Fourier Transform Explained with Examples    • 2D Fourier Transform Explained with E...  
• What is Negative Frequency?:    • What is Negative Frequency?  
• Laplace Transform Equation Explained    • Laplace Transform Equation Explained  
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