Fourier Transforms! Example problem part 2
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- čas přidán 29. 12. 2019
- In this video we finish our slightly harder Fourier transform example problem! We'll get more practice finding an equation for our function and see how far we need to go to get a reasonable solution. Yay, math!
NOTE: @3:54 it should be + sin(alpha*x) ((not minus))
Questions about this or other math topics? Leave a comment and let's tackle it together!
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Thank you Ma’am. Your video is really helpful to understand the topic of Fourier Transform which i am studying as part of pdes course at my university
yayy thank you for sharing, glad to hear it was helpful!
Great video, I'm in an online signals and systems class right now, and this video is exactly what I needed!
Oh good! So glad to hear it is helpful! 😄
thank you your lessons help a lot.....all the way from South Africa
Wow! Thats awesome, thank you for the kind words and for watching!
You are a math savage!
I'm used to seeing Fast Fourier Transforms and Discrete Cosine Transforms as DSP code, but I'm still absorbing the more traditional depiction. Thanks for your work!
Thank you! Glad you found it helpful!! Ohhh that is super cool, are there any libraries you'd recommend ?? I still have yet to see Fourier Transforms (or Fourier series) in code, would love to see how it's written!
@@JenFoxBot Hi Jen, sorry for the lateness of this response. Happy New Year!
When I've encountered Fourier transforms it's always been in code I didn't write and don't own and they're coded in environments specific to those processors, often relying on specific unique supporting hardware features so I can't really just cut and paste something as a decent example. However, I looked around a little and found a reference that may show you something of interest as it provides explanation of the underlying methods while using standard C type examples...
www.drdobbs.com/cpp/a-simple-and-efficient-fft-implementatio/199500857
One thing to remember with DSP math in general is that until recently, the computing cycles necessary to implement "ideal" equations were not always present or available at the price point of the gadget needing them so a number of Fourier family transforms have been devised which extract the desired frequency domain info but with lots of caveats. So long as those limitations are fully understood at design time, they're shortcuts to a solution which make the result possible. www.dspguide.com/ch8/1.htm and en.wikipedia.org/wiki/List_of_Fourier-related_transforms
I would also suggest taking a look at the DCT or Discrete Cosine Transform which is great at filtering data prior to compressing it and thus is part of the JPEG compression algorithm. en.wikipedia.org/wiki/Discrete_cosine_transform Thanks to the useage in JPEG compression and decompression, there is a great deal of write up on it including theory and permutations for optimization on processors although much of the written material is decoder centric and the encoders are often marketed code.
For the last 30 years I've designed DSP hardware for audio manipulation but generally I leave the magic of the software to wizards like yourself. I've designed a number of processor arrays which if built would have been the world's fastest publicly known supercomputer at that moment albeit specialized for DSP applications, but your math abilities leave me in awe as I can only aspire to seek them.
I cannot recommend any specific libraries, but I would highly recommend Pure Data which is a complete environment for digital signal processing that is free (MIT license) and it runs on, MacOS, Windows, and Linux boards like the Raspberry Pi. Pure Data has a huge user community and there is a wealth of knowledge available within it. There is also a more industrial strength analog called MAX MSP which is even more recommended for serious applications. Thanks again for your videos!
Would like to see you using the derivative property. Great video, love your hair
Thanks very much! 😄😄😄 Could you expand a bit on what you mean by the derivative property?
@@JenFoxBot The fact that : F(dx(t)/dt) = iω*X(ω). It would make this problem way simpler too
That was helpful 👌
Much love from iran♥️🇮🇷
awesome, so glad to hear!!
From my understanding Fourier transforms are used to solve for the frequency decomposition of a grid space defined function, so wouldnt our solution end up being a summation of waves with varying frequencies multiplied by weight factor coefficients? My understanding of how Fourier transforms might be wrong since I never studied the math behind it but I’m just confused by what the answer found in the video tells us
if it had been a little slower,It would have been better.... But overall good
can you help me with this equation of CEFS y(t)=t², 0
Thanks for the kind words! I have a policy that I don't do specific problems for folks cause I want yall to learn how to apply the general knowledge (and I don't have time ). Id suggest starting by drawing a plot and identifying the boundary conditions where you can set things to zero. Break up the integrals into chunks based on those boundaries (i.e. for t
First!
😄😄😄
I hate math 🤣🤣 because i was back in M3 (B.tech) 🤣🤣
Often when we hate something it is because we are afraid of it, and fear is most often due to the unknown. You can learn to speak language, so you can learn to do math! It just takes practice :)
@@JenFoxBot impressive 👍🔥
@@deepanshuchaudhary6354 thank you :)