Welch's method for smooth spectral decomposition
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- Опубліковано 25 лип 2024
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FANTASTIC video. I have been struggling with understanding the concept of Welch's method through textbooks and papers, but this conceptual introduction without any math makes all of it make sense now. Thank you!
Glad it was helpful!
Very clearly described, good presentation also.
Have finished watching "New ANT2". I finally understood DFT after graduated from school many many years. This serial of videos are the best in youtub to explain fundamental DSP for people like me without tones of mathematics background (CE major here). I can tell the author put a lots of though on how to explain clearly without involving intimidating math. Many engineers (including me) hardly need to deal with continuous analog signals. DFT is only thing we need and we don't care about all the calculus in the FT. Saddly most DSP tutorial videos out there are heavily calculus mangling which shut my brain off instantly. Such good serial videos I don't understand why so few views. thanks Mike.
Thank you, Chanson. That's kind of you to write! And it warms my heart on this chilly, wet Amsterdam afternoon...
@@mikexcohen1 really? I stayed 3 weeks there last year working in my previous company office. drank a lots of beer too. haha. cheers.
love the way you simplified the whole thing, i just wish you did matlab coding as well
Very good explanation. Thanks!!
this was really nice and clear! thanks!
Love your videos, thank you very much !
this is really amazing!
Thank you very much for this course!
You are a hero! Finally a to the point informative vid without the electrical engineering madness!
It's true: EE is pure madness!
Superb ! Thanks a lot !
Thank you!
Thank you, very clear explantion!
:)
great video! thanks
really helpful
best presentation about hann window and stfft I have ever reached
Thanks :)
Thank you
Thank you for the series of videos. Could you elaborate what kinds of non-stationarities the Welch method is robust to? or provide some reference to it? Thanks!
Sharp edges and sudden phase transitions are two examples of non-stationarities that have a bigger impact on the FFT than on Welch's method.
Wow ... such a great lecture! Thank you for sharing with us ... I have a question. If Welch's method is fundamentally applying FFT with short time window and averaging over time, then would I get the same result when I apply STFT and average it over the time dimension?
Yes, exactly correct: The STFFT averaged over all time points is essentially the same thing as Welch's method.
@@mikexcohen1 OMG it feels so great that you replied me back ... ! I had studied neural engineering and had a lot of help from your book ... ! Thank you for your reply ! That's so kind :)
Thank you for your videos. My task is to distinguish
between EEG in relax condition and EEG in mental arithmetic task. For each condition I have separate signals. Do you think that Welch's method is suitable for my problem, when the features would be band power, relative band power and so on?
look into short time fourier transform, its very similar
worth watching!!
As u mentioned that welch's method reduced spectral precision so can we use to plot spectral density ?? or fft is better?
I have a time series and want to find the period of that.
Well, you always use the FFT algorithm; it's a matter of whether you apply one FFT to the entire signal, or lots of FFTs on smaller segments of the signal and then average the spectra together.
@@mikexcohen1 thanks a lot
Will this method ignore frequencies that are too long for the smaller window?
Great observation! Indeed, that's true, and the limited spectral precision is part of the trade-off. You can select the time window based on the lower frequencies that you want to include.
5:56 This is done by multiplying the signal segment with the hamming window?
In the video I showed a Hann window, but Hann and Hamming windows are very similar.
I am currently enrolled to this course, but I cannot seem to find this video. Where would I be able to find this?
I believe it's lecture #80.
Thanks! A question though: at 7:15, the tapering reduces the average amplitude of the signal, so I'm assuming it also reduces the amplitude of the corresponding Fourier coefficients, right? Is that compensated for in Welch's method? Are the coefficients scaled back to match what we would have without tapering?
Yes, great observation. The attenuation of signal is one of the motivations for having successive windows overlap. For example, the edges that are attenuated by the taper in segment N can have minimal attenuation in segment N+1.
@@mikexcohen1 Uhm, ok, I see, thanks. I would have thought it would be something quite easy to compensate for, though. By dividing by the average weight of the window or something. (Assuming the weight to be a value between 0 and 1 if the window's peak amplitude is 1).
Yes, of course it's possible to compensate for the decrement in energy if you know the overlap and the window function. But honestly, in these kinds of applications, relative energy is usually more important than absolute energy.
@@mikexcohen1 Indeed. I see. Thanks again!
one more thing is that if the length of the segment is equal to total samples in pwelch then pwelch will become fft??
Yup, also assuming you wouldn't window the entire data series.
hi how are you?
good video thx good explained
Thanks!
If the snippets are 200ms, can I discover frequencies with a period of more than 200ms in the welch's method? Because as i understood, all low frequencies are tampered out. Is this what is meant with "reduces spectral precision"?
Nope, you'd need longer windows to detect lower frequencies.
I find this paradoxical. 2:24 We apply Fourier transform to figure out the frequencies.
Don't we use the fact that any periodic signal can be decomposed into its set of frequencies that make it, for Fourier transform?
So if frequencies f1,f2,f3 etc, are found to be present in the full FFT method, doesn't that mean that sin(2*pi*f1*t), sin(2pi*f2*t), etc are present every time? What am I missing?
This means that all the frequency components with their own amplitude were present at all instances of time, which is obviously wrong.
Each Fourier coefficient is like an average of the energy from the entire time window. If the signal is non-stationary, then the Fourier coefficient could take on the same value if there is low energy at f1 all across time, or a big burst of energy at f1 for only a brief period of time. That doesn't mean the Fourier transform is wrong (it's never wrong), but it will be harder to interpret for non-stationary signals.
@@mikexcohen1 Thanks for the response. I understand the workings of Fourier Transform (3b1b).
The FT tells you all the frequencies present in the complex but periodic input signal. So, by definition, when you apply FT to a certain window, the figured-out frequencies are to be interpreted as being present every time within that window.
In the case of full FFT method, the window size is the entire length of the input signal. I find it fundamentally wrong to apply FT if something is not periodic so as to interpret that all frequencies were present all the time. I missed that we had "constructed" a periodic one by concatenating itself infinite times.
I forgot it's true only for the artificially constructed version, but not for the aperiodic input signal.
Thanks! The video really helps.
Love your videos, thank you very much !