Infact, your videos are really good. They make you understand the course. Please do you have any videos on the inversion formula for awindowed Fourier Transform?
Hey, is there way of improving precision of the FFT without increasing computational complexity ? My problem is that the half of the FFT window results are only complex conjugates, meaning the resolution is halved, because useful frequencies are really only in the first half...
Hi Antagon. The "raw" output of the FFT is indeed complex-valued. Most people extract the power spectrum from that complex spectrum. I don't discuss that in this video, but it's in other videos in my ANTS2 series. As for increasing the spectral precision: Yep, you can do this by zero-padding the time series. I also talk about that in other videos ;) or you can look up "zero-padding theorem."
Thanks for such a good explanation. I have a doubt. How do we plot overlapping windows? Do we place them side by side but that would increase the length of time axis or take average/weighted average of two adjacent windows for getting power spectra of the common region of two overlapping windows? Kindly explain
The time windows may overlap, but the spectrum is plotted at the center time point. So as long as each time window is shifted slightly from the previous, the center time points will not overlap.
Thanks :) The slide template and color palette was designed by a professional science graphic artist. I made the graphs in MATLAB and then pasted them into the slides, but the MATLAB graphics have the same color palette with matching background, so you don't actually see that it's just a pasted screenshot, lol.
Why is "attenuation" of the window required? I simply applied the FT on "square windows" but then I realised everyone else would apply some window function, like the hanning function. How does it improve the accuracy?
That helps protect against sharp edges at the signal boundaries introducing artifacts in the spectrum. I wouldn't say that windowing is "required," but it is a good idea if the windows are relatively short.
Windowing makes the signal wrap around on itself (makes it "periodic") when you force it to taper down to the same values at the two edges, which makes the FFT behave much better.
Using a square window means that frequencies whose wavelength don't fit in that window will be more distorted than frequencies where many wavelengths fit. This is called spectral leakage. Applying a window reduces this negative effect, but distorts the results. Different windows have different advantages, so it's all about choosing a window that distorts in ways you don't care about. You could ofcause just use an infinitely long rectangular window, but that is just converting the STFFT back into the FFT.
Loved your video man. I just have one doubt at 5:55 the figure on the right is actually Multiple Resolution STFT right? Where I can have multiple resolutions for different frequency bands?
Yes, you can pick different spectral resolutions for different ranges of frequencies. It's more code to write and thus a bit more hassle ;) but yes that's what that picture illustrates.
That doesn't really happen in the Fourier transform. To get spectral overlap you'd have to use a different method, like wavelet convolution for example.
@@mikexcohen1 Correct. I collecting data on free time how to do time-frequency reassigned (TFR) spectrogram. Have pdf's and Python,libs. Now must understand how it works.
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Hands down this is the best tutorial for STFFT.
Awesome, thanks 😊
You're an incredibly talented teacher!
Thanks! I'm glad you found the video useful.
Thank you, Sir, for making such lectures available for all.
Most welcome
Infact, your videos are really good. They make you understand the course. Please do you have any videos on the inversion formula for awindowed Fourier Transform?
Wow! I like this! Highly recommended. Thanks!
Nice, thanks.
Hey, is there way of improving precision of the FFT without increasing computational complexity ? My problem is that the half of the FFT window results are only complex conjugates, meaning the resolution is halved, because useful frequencies are really only in the first half...
Hi Antagon. The "raw" output of the FFT is indeed complex-valued. Most people extract the power spectrum from that complex spectrum. I don't discuss that in this video, but it's in other videos in my ANTS2 series.
As for increasing the spectral precision: Yep, you can do this by zero-padding the time series. I also talk about that in other videos ;) or you can look up "zero-padding theorem."
It's a gem. Many thanks!
bhai merko 5:10 ke agae samjhade
Thanks for such a good explanation. I have a doubt. How do we plot overlapping windows? Do we place them side by side but that would increase the length of time axis or take average/weighted average of two adjacent windows for getting power spectra of the common region of two overlapping windows? Kindly explain
The time windows may overlap, but the spectrum is plotted at the center time point. So as long as each time window is shifted slightly from the previous, the center time points will not overlap.
@@mikexcohen1 Thanks a lot, Now I got it
Thank you for nice series video :)
Thanks for the videos! I'm curious, what do you do your plots with? I love the color palette!
Thanks :) The slide template and color palette was designed by a professional science graphic artist. I made the graphs in MATLAB and then pasted them into the slides, but the MATLAB graphics have the same color palette with matching background, so you don't actually see that it's just a pasted screenshot, lol.
@@mikexcohen1 Ahha, very creative! Excellent work :)
Why is "attenuation" of the window required? I simply applied the FT on "square windows" but then I realised everyone else would apply some window function, like the hanning function. How does it improve the accuracy?
That helps protect against sharp edges at the signal boundaries introducing artifacts in the spectrum. I wouldn't say that windowing is "required," but it is a good idea if the windows are relatively short.
@@mikexcohen1 makes sense, thank you for these videos
Windowing makes the signal wrap around on itself (makes it "periodic") when you force it to taper down to the same values at the two edges, which makes the FFT behave much better.
Using a square window means that frequencies whose wavelength don't fit in that window will be more distorted than frequencies where many wavelengths fit. This is called spectral leakage. Applying a window reduces this negative effect, but distorts the results. Different windows have different advantages, so it's all about choosing a window that distorts in ways you don't care about. You could ofcause just use an infinitely long rectangular window, but that is just converting the STFFT back into the FFT.
Loved your video man. I just have one doubt at 5:55 the figure on the right is actually Multiple Resolution STFT right? Where I can have multiple resolutions for different frequency bands?
Yes, you can pick different spectral resolutions for different ranges of frequencies. It's more code to write and thus a bit more hassle ;) but yes that's what that picture illustrates.
Thanks so much
enlightening, Thank you!
Ok, make Time Overlap is easy, but how to do Frequency Overlap?
That doesn't really happen in the Fourier transform. To get spectral overlap you'd have to use a different method, like wavelet convolution for example.
@@mikexcohen1 Correct. I collecting data on free time how to do time-frequency reassigned (TFR) spectrogram.
Have pdf's and Python,libs. Now must understand how it works.