What is a Discrete Fourier Transform (DFT) and an FFT?

Explains how the output of a DFT, and a Fast Fourier Transform (FFT), relates to the Fourier Transform of real-time signals. As pointed out in the video, note that the FFT gives the same output as the DFT - it's just a more efficient implementation of the function.
* 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.
Check out my 'search for signals in everyday life', by following my social media feeds:
Facebook: profile.php?...
Instagram: / iainexplains
Website: www.iaincollings.com
Related videos: (see www.iaincollings.com)
• How does the Discrete Fourier Transform DFT relate to Real Frequencies? • How does the Discrete ...
• Discrete / Fast Fourier Transform DFT / FFT of a Sinusoid Signal • Discrete / Fast Fourie...
• What is the Fourier Transform? • What is the Fourier Tr...
• What is the Fourier Transform used for? • What is the Fourier Tr...
• Fourier Transform Equation Explained • Fourier Transform Equa...
• Why do Periodic Signals have Discrete Frequency Spectra? • Why do Periodic Signal...
• Discrete Time Basis Functions • Discrete Time Basis Fu...
• How are the Fourier Series, Fourier Transform, DTFT, DFT, FFT, LT and ZT Related? • How are the Fourier Se...
• OFDM and the DFT • OFDM and the DFT
• Fourier Series and Eigen Functions of LTI Systems • Fourier Series and Eig...
• Discrete Time Basis Functions • Discrete Time Basis Fu...
• Is Phase important in the Fourier Transform? • Is Phase important in ...
For a full list of Videos and accompanying Summary Sheets, see the associated website: www.iaincollings.com

[@user-zr8vi4im9q]

Thank you so much sir, it helps my final week!

[@iain_explains]

I'm glad to hear it. Good luck - it sounds like you've got exams coming up.

[@fishgrey6441]

Thank you very much for your explaination about the DFT. Back in my college year, my DSP teacher just told us periodical in time domain is discontinuous in frequency domain and so on. Your video builds a link between those abstract concept and is really helpful to me. By the way, would you please consider making a video about the windowing, such as the Taylor window, Chebyshev window...

[@iain_explains]

Thanks for your comment. You've read my mind - I was actually planning to make a video on windowing, but realised I needed to first have a video explaining the DFT. So you can expect to see a video on windowing in the next couple of weeks. 😁

[@bahramhedayati423]

Is the FT of sin function drawn correctly?

[@iain_explains]

Yes, but I've only drawn the magnitude. I haven't shown the phase shift.

[@iahmad1857]

Thanks for the content. However, I watched the video only to learn what's FFT, but you didn't explain it.

[@iain_explains]

An FFT does exactly the same thing as a DFT. It’s just an efficient implementation of the algorithm. The details of the algorithm’s internal implementation are tedious and not really conducive to a video. Anyway, this video is about what it does, not how it’s implemented.

[@AJ-fo3hp]

​@@iain_explains With kind, I would like to correct the phrase in reply what you have provided " It is just an efficient implementation of algorithm" Correct phrase is as below "FFT is an efficient algorithm for implementing DFT". FFT effectively reduces time and memory taken to compute the DFT (each frequency component (N point) of Discrete signal) DFT is formula for computing each frequency component (N point) of Discrete signal. FFT is algorithm for DFT.

[@iain_explains]

You haven't "corrected" me. You've simply re-stated what I said!

[@AJ-fo3hp]

@@iain_explains you written ".. an efficient implementation of algorithm" FFT is not "implementation of algorithm" FFT itself algorithm for DFT. If somebody finds better algorithm for DFT than FFT, in terms of better computing in terms of "time and memory" or in any other way,then we call by different name(other than FFT) for that algorithm for efficient implementation of DFT. Fast Fourier Transform is an algorithm. The FAST name comes its redcution in time took to compute the DFT.

[@olaguibel27]

@@AJ-fo3hp There are other algorithms you can make to calculate the DFT, the FFT is 'simply' one that does it in an efficient manner. You haven't corrected anything, just restated what was already implied...