Parseval's Theorem
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- Опубликовано: 7 авг 2024
- Parseval's theorem is an important result in Fourier analysis that can be used to put guarantees on the accuracy of signal approximation in the Fourier domain.
Book Website: databookuw.com
Book PDF: databookuw.com/databook.pdf
These lectures follow Chapter 2 from:
"Data-Driven Science and Engineering: Machine Learning, Dynamical Systems, and Control" by Brunton and Kutz
Amazon: www.amazon.com/Data-Driven-Sc...
Brunton Website: eigensteve.com
This video was produced at the University of Washington 
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It's Plancharel's theorem BTW not Parseval's
Great point! I didn't realize that Parseval is for 2-pi periodic functions (i.e. for the Fourier series), while Plancharel is for the continuous generalization (i.e. for the Fourier transform). Thanks for pointing this out.
In the context of Fourier Transforms, they are pretty much the same. Plus, the equality statement in the beginning of the video is a statement from Parseval's Theorem.
#Now I have seen on Google that Plancharel's Theorem is used in non-periodic continuous functions (i. e. of Fourier transform) but in case of Fourier serias we use Parseval's Theorem (i. e. periodic). It is from engineering approach so I comment Parseval's Theorem vs Plancharel's Theorem. But in my opinion it can bring many problems for findind a power in a long, not small, periodic waveform dispersion.
I'm astounded that you offer so much insight into this topic with this playlist and explain it so good. It's free and better explained than some paid courses, I'm really thankful for that :D
Thanks a lot for making this material.
This was really well explained. Thanks!
Thank you again, greetings from the other UW (University of Waterloo)
THANK YOU!!!
Best play list of fourier transform so far....
Many thanks!
Great explanation! Can anyone point me to a place where this theorem is related for other transforms? E.g. such as the cosine transform?
why are u such a legend?
love you and peace bro!
Peace!
Thank you sir
If you listen carefully he says your name at 0:39
lol
hmm thats weird, I heard mine at 0:35
thats weird, I heard mine at 0:06
First like, then watch.
I wondered for a bit, is Steve left-handed? Then I created this scenario on my head trying to understand, my first guess is yes, he's indeed left-handed. Anyway, I'm loving the series, I will indeed watch all the videos on all the playlists! Good to see there are people willing to make others learn. Thank you.
#Now I have seen on Google that Plancharel's Theorem is used in non-periodic continuous functions (i. e. of Fourier transform) but in case of Fourier serias we use Parseval's Theorem (i. e. periodic). It is from engineering approach so I comment Parseval's Theorem vs Plancharel's Theorem. But in my opinion it can bring many problems for findind a power in a long, not small, periodic waveform dispersion.
Why is energy defined as integrate of square of signal function? 3:40
That's one way to measure a signal (you can also measure by their power, if the energy is infinite).
The phisical meaning is that if you have a load of 1 ohm and x(t) is your voltage or current (V=R*I, if R=1 => V=I), the energy calculated is the energy that dissipates in that load.
@@miguelmondardo2741 thank you. But i didnt understand your answer
Aren't all numbers the same?
Energy, ie. the conserved quantity, is not in the integral of the norm, it's in the integral of the norm squared. Huge difference. Why be this sloppy?
#parsevalmusoc
Hold On Hold On. Is this necessary for Data Science?
If you want to compress your data and have any guarantee on the fidelity of your reconstruction, then yes.
Is he writing backwards or is this some videography trick?
Video trick
are you writing backward or are finals finally getting to me
yo this is breaking my brain too
Bhaiya kuch samajh nahi aya