I have enjoyed the previous videos. The explanation was great. In this video, some concepts were not explained. It was tough for me to understand. What helped me was watching the video from the 3 Blue 1 Brown channel "But what is the Fourier Transform? A visual introduction.". That video was awesome. It connected all the dots for me. Hope it helps others as well.
What I like about your way of explaining is that all the steps are about the same size (as in: equally complex) which makes I very easy to follow. Well done!
You are a good teacher. I came here to understand how voice recognition works. I'm halfway to finishing the video series and you have somehow bridged a gap for me i have struggled with, equations. I feel like i really understand how to read the equations now in a way i can digest and process it as before it was just a bunch of Greek symbols and operators bunched together somebody says is a proof.
Thank you for such a nice explanation. I only couldn't catch one step: Initially we had defined d_f and phi_f using max and argmax expressions. However, at the end we just defined them again as components of the complex fourier transform. I missed how that derivation ensures that d_f is maximum and phi_f is an "optimal" phase, as originally defined. Thank you.
Really great question. I know this is 2 years late but here is my understanding: It really comes down to the absolute brilliance of complex exponentials. Previously, we were simply integrating a sinusoid multiplied by our signal. This allowed us to only capture the "strength" at a specific phase, and then (as you said) we had to find the phase that made that strength a maximum. With the complex fourier transform, you can think of it as us rotating both a sine wave AND a cosine wave. A cos wave is simply a sine wave shifted 90 degrees to the left. Since e^(i * 2pi * f * t) = cos(2pi * ft) + i * sin(2pi * ft) the part of the signal that more aligns with the cosine will be "picked up" in the real part, and the part that most aligns with the sine will be picked up in the imaginary part. The phase of this complex number is *exactly* the optimal phase, because it has "searched" through the signal using two sinusoids maximally apart from one another, thereby "splitting" the signal into real and imaginary parts *according* to its phase. I hope this makes sense. When we take the magnitude of this complex number, we "automatically" get the maximum magnitude, since it has "picked up" both phases (0 and -90) of the signal, which does capture the *total* strength. Hope this helps!
Thank you Valerio for this wonderful video!! I've been struggling with CFT for a long time and this made everything so much clearer and now I'm very excited to say that I'm starting to get it :D
a little more explanation of " g^ (f) = C_f = (d/root(2)) * e ^ ( - i * 2 * PI * f * t) => (?) integral( g(t) * e^( - i * 2 * PI * f * t) ) woyuld be great..! You explained through practical visualization how the C_f and g^ (f) is similar but I am getting stuck whenever I am trying to go deeper here. Thanks..!!
Hello, thanks for the amazing videos. I have one question, if you'd be able to answer: at 13:39, I don't understand where the g-hat of f question comes from. How do we derive it? Thanks in advance.
I have a doubt in Fourier transform. .While taking Fourier transform, as you explained , we get a sort of curve in the complex domain. How is this connected to complex frequency Cf. I suppose that this Cf (Cf is always a single point) has only one component for f=1Hz since the pure tone is of 1Hz. It is mentioned that the curve is obtained when the signal g(t) is grabbed inside the exponential signal.Is it my mistake? Does the curve represent g(t)* exponential(-i*2*pi*f*t) for f=1,2,3 Hz (the original signal has three components) or does that represent the curve g(t)* exponential(-i*2*pi*f*t) for f=1Hz. I am a bit confused why this much points are generated for a single/three frequency. We saw several curves, for t=10sec length ,we saw a big curve ,whereas for t=1sec, we saw a small one which will subsequently become that big one by changing t=10sec. I think so we have only one component for Cf at a particular time step of 1/1000sec. Next point for another time step of 1ms , is it like that we are getting a large number of points due to time steps and not due to frequency? My doubt is, can I get any relation between the curve and the frequency 'f' because in inverse fourier transform, at time 40:40 in the video, we are actually integrating different Cf components. While integrating , it is being explained as adding in frequency. How did three signals come there?
Hello Velardo! Recently I’ve watched your video on business use cases of AI music generation, thanks for the inspiring introduction! Actually I’m personally more interested in music information retrieval (MIR), so could you please elaborate on it? (Eg. business use cases; whether it requires solid music background knowledge/skill; related academic programs etc.) I’d appreciate it so much!
I was wondering what kind of engineering degree you might need for audio signal processing. You sound like you had a math related background. I suppose that should be the right degree for becoming an expert in this field.
You can get at it from different directions. Anything that has to do with CS, electrical engineering, physics, math will do. Programming is fundamental though.
First of all, thanks for the amazing helpful videos. Secondly, Wasn't there a circular argument? To obtain g^(f) we need to calculate the phase and the magnitude but in order the obtain the phase and the magnitude we need to calculate g^(f). What am I missing?
Sir, thanks a lot for these great videos. On question though : what’s the motivation of transforming the two initial equations to equations with complex number inside. I mean why we didn’t continue using the sin.
@@maddai1764 indeed! The complex notation is just more elegant, and widely adopted. As a general hint, everytime we deal with rotations and periodic signals, complex numbers come in handy ;)
So basically we can describe a piece of music "just" as a combination of all the possible sinusoids with frequencies we can hear, each multiplied by a peculiar envelope in time.
I have enjoyed the previous videos. The explanation was great. In this video, some concepts were not explained. It was tough for me to understand. What helped me was watching the video from the 3 Blue 1 Brown channel "But what is the Fourier Transform? A visual introduction.". That video was awesome. It connected all the dots for me. Hope it helps others as well.
Thank you. I studied this in Uni but never fully grasped it as well as I have after watching your videos. Thanks.
What a video and explanation. Specially when you plotted the fourier transform for different pure tones it blew me away. Gonna watch the video again
This is Amazing! Every teacher that teaches this subject should watch this video!
thank you so much brother, i don't know why people make it look like it's impossible to understand. You did an amazing job of explaining it
What I like about your way of explaining is that all the steps are about the same size (as in: equally complex) which makes I very easy to follow. Well done!
Thank you!
Those complex equations turned simple after you explained each bit. The visualizations also helped a lot. Thanks for the whole series. Great job!!!
Thank you Clarence! I'm happy you find the series instructive :)
Good learn more on my channel
You are a good teacher. I came here to understand how voice recognition works. I'm halfway to finishing the video series and you have somehow bridged a gap for me i have struggled with, equations. I feel like i really understand how to read the equations now in a way i can digest and process it as before it was just a bunch of Greek symbols and operators bunched together somebody says is a proof.
Best explanation, 10000000000x better than my maths teachers
Thank you for such a nice explanation. I only couldn't catch one step:
Initially we had defined d_f and phi_f using max and argmax expressions. However, at the end we just defined them again as components of the complex fourier transform. I missed how that derivation ensures that d_f is maximum and phi_f is an "optimal" phase, as originally defined. Thank you.
Really great question. I know this is 2 years late but here is my understanding:
It really comes down to the absolute brilliance of complex exponentials. Previously, we were simply integrating a sinusoid multiplied by our signal. This allowed us to only capture the "strength" at a specific phase, and then (as you said) we had to find the phase that made that strength a maximum.
With the complex fourier transform, you can think of it as us rotating both a sine wave AND a cosine wave. A cos wave is simply a sine wave shifted 90 degrees to the left. Since e^(i * 2pi * f * t) = cos(2pi * ft) + i * sin(2pi * ft) the part of the signal that more aligns with the cosine will be "picked up" in the real part, and the part that most aligns with the sine will be picked up in the imaginary part. The phase of this complex number is *exactly* the optimal phase, because it has "searched" through the signal using two sinusoids maximally apart from one another, thereby "splitting" the signal into real and imaginary parts *according* to its phase. I hope this makes sense.
When we take the magnitude of this complex number, we "automatically" get the maximum magnitude, since it has "picked up" both phases (0 and -90) of the signal, which does capture the *total* strength.
Hope this helps!
thank you, Valerio. Your videos are amazing. It's exactly what I was looking for.
You're welcome!
I love your explanations with just right amount of maths, thank u so much sir
Thanks!
You r next to god sir,love from India
This is a gem. Thank you Valerio!
Thank you, this series helped me with my engineering project a lot
Thank you Valerio for this wonderful video!! I've been struggling with CFT for a long time and this made everything so much clearer and now I'm very excited to say that I'm starting to get it :D
Bro Thank you so much , for taking so much effort and helping us to understand these complex things in a easy way. This is just a master piece
Amazing! Thanks for the clear explanation of such a difficult topic.
These lectures are amazing!!! Thank you so much, I finally understand audio signals clearly
great explanation! Thanks
Sir Thank you for this lecture. Really helping me to brushing up my knowledge. Looking forward to DFT
Thanks Hardy :)
Good Learn more on my channel
thanks Valerio, it is a great tutorial. I have a question. Df was idefined in the previous as duration, but in the video as magnitude.
Fantastic Explanation!
a little more explanation of " g^ (f) = C_f = (d/root(2)) * e ^ ( - i * 2 * PI * f * t) => (?) integral( g(t) * e^( - i * 2 * PI * f * t) ) woyuld be great..! You explained through practical visualization how the C_f and g^ (f) is similar but I am getting stuck whenever I am trying to go deeper here. Thanks..!!
Hello, thanks for the amazing videos. I have one question, if you'd be able to answer: at 13:39, I don't understand where the g-hat of f question comes from. How do we derive it? Thanks in advance.
this is perfect
thanks so much
I have a doubt in Fourier transform. .While taking Fourier transform, as you explained , we get a sort of curve in the complex domain. How is this connected to complex frequency Cf. I suppose that this Cf (Cf is always a single point) has only one component for f=1Hz since the pure tone is of 1Hz. It is mentioned that the curve is obtained when the signal g(t) is grabbed inside the exponential signal.Is it my mistake? Does the curve represent g(t)* exponential(-i*2*pi*f*t) for f=1,2,3 Hz (the original signal has three components) or does that represent the curve g(t)* exponential(-i*2*pi*f*t) for f=1Hz. I am a bit confused why this much points are generated for a single/three frequency. We saw several curves, for t=10sec length ,we saw a big curve ,whereas for t=1sec, we saw a small one which will subsequently become that big one by changing t=10sec. I think so we have only one component for Cf at a particular time step of 1/1000sec. Next point for another time step of 1ms , is it like that we are getting a large number of points due to time steps and not due to frequency? My doubt is, can I get any relation between the curve and the frequency 'f' because in inverse fourier transform, at time 40:40 in the video, we are actually integrating different Cf components. While integrating , it is being explained as adding in frequency. How did three signals come there?
Hello Velardo! Recently I’ve watched your video on business use cases of AI music generation, thanks for the inspiring introduction! Actually I’m personally more interested in music information retrieval (MIR), so could you please elaborate on it? (Eg. business use cases; whether it requires solid music background knowledge/skill; related academic programs etc.) I’d appreciate it so much!
Thank you for the comment Jlafeng. I'll definitely cover the topics you requested in future "Tips and Tricks" videos.
Good learn more on my channel
Comment for promotion! Thanks for the video!
Sir once you explain wavenet and tactron for speech synthesis as well please
I'll probably cover those in the future.
What is this C_f where did it come from?
I was wondering what kind of engineering degree you might need for audio signal processing. You sound like you had a math related background. I suppose that should be the right degree for becoming an expert in this field.
You can get at it from different directions. Anything that has to do with CS, electrical engineering, physics, math will do. Programming is fundamental though.
mindblowing
Why is it we don’t need to optimize the phase when using complex numbers?
First of all, thanks for the amazing helpful videos.
Secondly, Wasn't there a circular argument? To obtain g^(f) we need to calculate the phase and the magnitude but in order the obtain the phase and the magnitude we need to calculate g^(f). What am I missing?
you always need one for the other.
Great content thanks !!!
Sir, thanks a lot for these great videos. On question though : what’s the motivation of transforming the two initial equations to equations with complex number inside. I mean why we didn’t continue using the sin.
That's done in order to have a compact notation for the FT. A complex number allows us to express a FT coefficient with a single (complex) value.
@@ValerioVelardoTheSoundofAI thanks for the response. So it’s not the only way, I mean one could use the original equation.
@@maddai1764 indeed! The complex notation is just more elegant, and widely adopted. As a general hint, everytime we deal with rotations and periodic signals, complex numbers come in handy ;)
@@ValerioVelardoTheSoundofAI very clear. Thanks a lot. Continue the good job pls.
Do you have any Idea that these videos are a revolution on math pedagogy haha? Thanks!
Thank you Diego :)
olha ai kkkk
So basically we can describe a piece of music "just" as a combination of all the possible sinusoids with frequencies we can hear, each multiplied by a peculiar envelope in time.
Yes, that would be the lowest-level description of a musical piece.
COOL!
the tutorial is just unnecessarily long; could have been finished in 25 mins quite easily
Man, this guy has so many distracting quirks. How can you guys actually concentrate on the content?? xD