Discrete Fourier Transform (Part 2 - Windowing)

[@ammarzain4877]

This video is straightforward to follow if we want to know DFT (windowing technique). It helps me understand the intuition of windowing + DFT as general. Thank you!

[@QuantitativeBytes]

Glad it was helpful!

[@kaxxamhinna5044]

Great pedagogy! Thank you very much sir

[@eliasvusi3451]

You have certainly dropped this to my level, thank you. Is it a right observation though if I say, for the chosen shortened signal, the FFT would have given a single spike at the correct frequency & the illustration is more on the inappropriateness of the application of the rectangular window for the signal in hand?

[@deusex4686]

thank you for making this great video, i am really interested in it, but i didn't find part 3 of it,really hoping for the video of using DFT and windowing to do time frequency signal analysis. thanks again for the great explanation!

[@QuantitativeBytes]

Thank you very much for your comments! I continued from this video with a series looking at creating a simple spectrum analyser app. The playlist for that is here: kzbin.info/aero/PL3WoIG-PLjSuom-Xl0M1pspvqK1RfKlBn This might not be exactly what you are looking for, but should cover everything you need to do time-frequency analysis. I am planning to come back to this topic at some point, so I might make more videos on time-frequency analysis specifically then.

[@sharshabillian]

I see the Hanning window gives smaller side-lobes, which leads to less leakage between nearby frequencies, compared to a rectangular window. However, the Hann window in this case has a significantly larger main lobe. Does this not lead to mixing up close frequencies when convolved in the frequency domain?

[@fernandotezza1335]

Great content and phenomenal visualization :)

[@QuantitativeBytes]

Thank you very much for the comment! Glad you enjoyed the video.

[@IsaacMorton]

This all makes sense, thank you. I was however wondering, could all this be avoided by simply taking the Fourier transform starting at 75 and ending at 375 instead of computing the fourier transform of the full 0-500 range? In my mind this would produce a less accurate representation, as there are less points, but would avoid the windowing artifacts.

[@rezhaadriantanuharja3389]

Ideally yes, it's best to apply Fourier Transform to one period of your signal. In real world application, however, the signal may consist of multiple frequencies which we don't necessarily know. Another thing to consider is, the speed of computation: If you perform DFT to a vector of length 301 (as you mentioned by starting at 75 and ending at 375), you need to compute a new set of basis vectors because different vector lengths have different set of basis vectors. If your vectors always have the same length e.g. 512, you only need to compute the basis vectors once then store it in memory for future use. This is particularly useful for application such as mobile vibration monitoring device. If your vector length is a power of 2 e.g. 512 or 1024, you can use Fast Fourier Transform algorithm which will give you O(N log N) instead of O(N x N). That being said, common practice is to use various window functions e.g. Hanning Window and then apply Fast Fourier Transform to a vector of length 2^m.

[@euglossine4ever]

So useful and digestible Tysm

[@QuantitativeBytes]

Thank you very much for the comment, I'm glad it was useful!

[@MoXyiD]

Another awesome video! Id love to see more content about various filters, and maybe even statistical DSP! ^^. Z-transform would be awesome, maybe some constellation content ^.^ I could go on and on. Thanks a bunch.

[@QuantitativeBytes]

You're very welcome! And thank you for the comment - those are some good ideas! I'm on a bit of ray tracing theme just now, but I might come back to signal processing at some point.

[@GGutierrez]

Thank you . Keep going.

[@QuantitativeBytes]

Thank you, I will!

[@alexis-74]

you are a genius

[@QuantitativeBytes]

Oh, I don't think so, but thank you very much for saying so!

[@Mr.Nichan]

What I don't understand is why people take the DFT of the whole signal with only one part non-zero, introducing all kinds of nonsense data because you (for no good reason) mandated that the rest of the function must be zero, when you could just as easily ACTUALLY just take the DFT of the window (i.e., treating the part of the signal in the window as if it were the entire signal, with a smaller number of samples), which means not caring at all what what nonsense values the DFT would imply occur OUTSIDE that window.

[@conrisc]

Briliant, thank you

[@QuantitativeBytes]

You're very welcome! Thank you for the comment.

[@burakkara337]

Thank you, great explanation

[@QuantitativeBytes]

You are welcome!

[@jollychappies]

Really well made video and really insightful. I'm currently doing coursework on this. Could you possible elaborate on how the DFT outputs of the rectangular window function and the input signal combine or 'convolute' to produce the leaked DFT signal? Or what can you suggest I put into google to learn this in the best way? Thanks a lot! Fantastic video. I've subscribed.

[@QuantitativeBytes]

Thank you very much for your comment and for subscribing! The term you want to search for is 'convolution', I think there are some fairly good explanations out there. Best of luck with your coursework!

[@Funtoosh5395]

thanks a lot sir ..this is first time, even from non electronic background I understand this ....but technical term should be present in video bcos sometimes we don't get the term...even subtitles misspelled it

[@QuantitativeBytes]

You're very welcome and thank you for the comment!

[@samirelhalabi6876]

Thank you so much!

[@QuantitativeBytes]

You're welcome!

[@mohanraj411]

very useful .Thanks a lot . can u explain about Z transform relation with DFT

[@QuantitativeBytes]

You're very welcome, glad you found it useful! I will think about looking at the z-transform for a future video, thanks for the suggestion.

[@rajabmur4311]

Thank you so much, that was really helpful, i just have a question, how could i choose the best window for sampling, in this example the Hann window was better, in other signals it will not?

[@sonnenhafen5499]

depends on your requirements to the sidelobes and bandwidths... here you have some names you can put into google: hanning, hamming, blackman, kaiser(!!) window. these are things you learn in some courses on digital signal processing or filter design for M.Sc. on technical uni, keep that in mind, if there are some things overwhelming you. have fun

[@bertproeme4535]

FFT? RF frequency's

[@QuantitativeBytes]

Indeed. FFT of course the way to go for a practical implementation. The content here is intended to be educational on how the discrete Fourier transform actually works, rather than the most efficient implementation. Plenty of good FFT implementations out there already, so I didn't see the point in repeating those.