Demystifying the Fourier Transform: The Intuition
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- Опубликовано: 30 июл 2024
- I explain how the Fourier Transform works. I avoid getting into the mathematical intricacies (for now!). Instead, I focus on the intuition using a visual approach. The Fourier Transform is a fundamental tool used in audio signal processing for extracting information from audio data, and transform a signal from the time to the frequency domain.
Slides:
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Code:
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This is the best Fourier Transform class I've ever watched!!
Thank you very much Valerio!
Thanks Gildo!
These video are helping me so much in understanding Audio Processing! Thank you so much! This has so so much value to me.
One year before my graduation as a computer science eng, two years ago, I spent a semester trying to understand FFT from lectures, no surprise it didn't work, but now it all makes perfect sense, Thank you for all your effort
Glad I could help :)
what a beautiful class! You are doing amazing Valerio! I am grateful and thanks a lot for all the efforts you put in this lovely lecture series
I really appreciate the effort you must have put in Valerio, Great content ! Keep up the good work. Your channel is one of the best in audio machine learning out there.
Thanks Siddhant!
Love all the valuable videos you've made. Amazing insights & applicable
Your explanations are great. This is one of my favorite channels.
Thanks a lot JawadQ1 :)
I just binge watched the whole series over New Years and I'm just blown away-incredible content and presentation. Thanks Valerio! All the videos are great but I found this one on the Fourier Transform just magical. Keep up the excellent work...it is very appreciated 🎉
Thanks a lot Thomas!
From Brazil. You're the man in audio processing knowledge! Thanks a lot!
Simplest and most intuitive explanation of FFT I've seen. Fantastic job!
Thank you Austin!
Very clear video for this tough concept. Thank you so much for this. Every book i picked for deep learning had only images and so audio was magic to me till I watched your videos.
I am really impressed how good you explained it. This helps to put concepts and intuitions from different sources together. Especially that you introduced FT as maximization problem.
Thanks!
Awesome explanation and eagerly waiting for your next video as usual in the weeks, Cheers
Thank you Venkatesan! Next video will be out on Thursday, as usual ;)
I must say I really love the way you teach and make me work in a better way for Audio Recognition Project.
Thank you Shubham!
I always found FT very tricky but you explained really well. Thank You!
Where were you when I was at radio school a million years ago??
Great tutorial!! Thanks
Just one word....INCREDIBLE!
Awesome job - thanks so much for putting this together.
Excellent video. Thank you for the explanation.
I do have a concern about your sine wave formula, and maybe somebody has already mentioned this, or maybe you talked about it and I missed it. If you want phi to be equal to the phase shift in your sine function, the horizontal scale factor (2pi•f) must be shown as a coefficient on the binomial (t - phi), as horizontal dilation is done before horizontal translation (otherwise the dilation changes the translation), and when shown in with the variable, must be written in the opposite order (last transformation closest to the variable). The way you have represented your sine function in this problem, the true phase shift would be phi/(2pi•f).
Contrary to most physics texts, I find it more straightforward mathematically to let phi represent the true phase shift and show the argument of the sine function as 2pi•f(t - phi). Some physics texts and math texts do this, but not many. Having taught college algebra many times, I think this format is more consistent with the logic of transformations of parent functions, and therefore more conducive to a deeper understanding of the geometry of the sine wave. But, to each their own, I suppose.
Man I have read so many FTs , I know how "Fast" is based on log and the idea of recursion and the matrix reduction and all that to use in Mel freqs and all but I have never seen an explanation as good as this.
This makes complete sense. This is awesome, instead of AI/ML it almost makes me want to go back to collage and do a phd on math(maybe I am pushing it)
Thank you!
Thank you for this! Your content is amazing
Thanks Valerio, finally Fourier transform makes sense to me.
Nice!
No words. well articulated
this video is fantastic! thanks a lot
amazing video sir , subscribed!
You rock man. Thank you so much !
Great Work. Tank you very much
Thank you so much !!
Great video
loved it
thank you!!
Thank you :)
Interesting interpretation form to a classical FT view (25:05)!
Hi Valerio,
This playlist is AWESOME! Thanks for your efforts. I do have a question in the code. When we zoomed in to the waveform
plt.plot(t[10000:10400], signal[10000:10400])
Why did you choose sample number 10000 as a starting point?
hervorragend!
Could someone please explain why Valerio defined frequency=np.linspace(0, sr, len(magnitude)) ?
Why do the values get to the sampling rate and why are the steps by the length of the magnitude array?
You rock man, i’ve been coding and reading about fft’s here and there. Never had understanding about basic principle. Though it begs a question, how do animals process complex sounds? Does it matter that we have two ears? Do we have internal fft?;)
Thanks for the amazing video, I just had a question about the part in the python code where you explained setting the range of frequencies for the FT. You stated that the range of frequencies on the x axis is between 0 and the sampling rate. Shouldn't it be between 0 and the Nyquist frequency? Would be great if anyone else could clear up this minor question as well. Thanks!
Hello, incredible series, very clear explanation so far.
I just have a question, but maybe in future videos I will found an answer.
I understand that we can go from frequency domain to time domain. But don't we miss the time information?
I mean, I understand for a short sound that we can decompose it and recreate it easily, but is it the case for a long audio?
As we don't have information from the time, we will have as an output of IFT only one constant signal? And maybe not a blank if we have two separates notes?
Thank in advance for your help :)
I agree, I have the same question: If the pianist is playing musical scale, we have spectrum of sounds. But in case we reproduce sound from this spectrum we got simultaneous sound of 7 musical notes, that is musical chord, not a musical scale.
When we apply foourier transform for a particular sine wave with certain frequency and phase can we have negative area?If yes then how is it represented in the frequency spectrum.
is it possible for the magnitude of the fourier transform to be negative?
9:26 isn't the X axis should be twice shorted than the signal length, fft is vertically mirrored so the right part of the plot is redundant
hello sir, what is the relative phase. and hod do you obtain it when doing inverse fft. because you only calculated the magnitude and frequency when dong the FFT.
is the relative phase the optimal phase that maximises the area that you calculated when doing fft do we store the phase somewhere like in an array and use it for inv fft in future?
Just wanna make sure my understanding is correct: @30:21, we can basically delete the "max" part of the d_f function, if we just plug in the optimal phase value right?
grazie
Prego :)
my signals look way different once i started on crearting the sine wave which also affected the phase value. is this normal?
i didnt really get a smooth corrolation as stated
Can you please suggest a book for Audio Processing for absolute beginners, I want to learn Audio processing for ML applications
Can someone tell me why @14:55 we multiply the sine wave function with 0.5? It seems like it controls the max and min amplitude of the resulting sine wave? Is there a reason why this is 0.5 or can it be set to just 1?
.5 is the phase of the sin wave as a percentage where 2π = 1, π=.5, and 0=0
@@KingQuetzal Thanks! But what is the phase variable for then? :)
@@Waffano Weird I must have looked at the wrong time. Yeah 0.5 is the amplitude multiplier. A normal sin wave is from -1 to +1 while the one generated at 15:28 is from -0.5 to +0.5.
I am waiting for the next vedio
I've already published a few in the series since this one!
@@ValerioVelardoTheSoundofAI I watched all the previous vedios
@@bangladeshisingaporevlog9273 what I meant is this isn't the last! There are new ones already...
hi what is the magnitude unit?
4:12 after fourier transform, X axis is frequency but what is the Y axis?
Its magnitude. In other words: The area of the combined curve of s(t) and the sinusoid at a specific frequency.
notebook is not working on the gooogle colab, >?
Not sure what's not working, but I haven't tried this in Colab.
i hope you start a serie for python just python please
It's annoying that only the left side of my headphone is working. Is it just me?
28:30 What is 'd' in the equation? Great video by the way!
Sorry, the answer came a few seconds later... magnitude.. :P
34:50
very very good example , but dont make it again please professor :)
please add video quality option 144p