Is Phase important in the Fourier Transform?
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- เผยแพร่เมื่อ 12 ก.ย. 2024
- Uses an example to demonstrate the role and importance of phase in the Fourier transform.
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Can’t express how much this helps. These abstract concepts are sometimes hard for me to wrap my head around but seeing you work through it slowly, starting from phase, and then adding phase, helped me internalize what the phase actually means for the transfer function. Thanks so much!
I'm so glad to hear that the video was helpful.
As soon as I realized I needed this video about two hours ago, I've been looking for an explanation, and this one is excellent! Perfect timing! Thanks
Glad it helped!
Your explaination is great and one thing I really like, you remind some key, simple concepts instead of saying "we already done in previous video".
Glad it was helpful, and I'm glad you like the approach.
I've had many signals classes and no professor made this point about phase so clear with application of linearity etc.
Glad you found it useful.
I've passed the DSP course last semester but after this video I realize that i did not understand it so well ...
Thanks to you anyway ...
Glad you've found the video useful. You might like to check out the other videos on the channel too.
You sir, are a life saver. This afternoon I have to take a test about this concept.
Glad you found it helpful. Good luck in your test.
This is such a great lesson. I tried so hard to put this concept into my mind and then I see your video.
You're greatly didactic!
I'm so glad it was helpful!
Sir, I must say you are a very good teacher. The simple, lucid way you explain things is a gift of God. It really helps us to understand such complex topics in a limited time. I wish you teach all subjects :D.
May I request you to cover Digital Modulation techniques like ASK, FSK, PSKs(QPSK, OQPSK, MSK) APSK, QAM and their choice of application? Error Correcting codes, esp the newer ones like LDPC, TPC.
Thank you, Sir
Glad you like the videos. Thanks for your suggestions. I've added them to my "to do" list.
This is so helpful and simple. Thanks!
Glad it was helpful!
Thanks! The flow of your explanation is simply amazing
Glad it was helpful!
Great video! Very clear and too the point! Thanks Sir.
Glad it was helpful!
you made it very simple
thx again
Glad it helped!
What a TEACHER you are!!!
Thanks. I'm glad you like the videos.
Thank you for this brilliant, intuitive and absolutely useful video
I'm so glad it was helpful!
thanks!
Hi Sir, thanks for your great video. I have a question about the phase cancellation. Is the reason that they can cancel each other because the shapes of the sinusoid wave component at the frequency at π/T for x(t - T/2) and the sinusoid wave component at the frequency at π/T for x(t - 3T/2) in time domain are flipped due to the phase, and they have the same amplitude and frequency, so the waves cancelled each other and no contribution at that frequency to the added new function, therefore the amplitude at that frequency of the new function is zero? (Just like the way you explained in Fourier Transform of Cos with Phase Shift?)
I'm not exactly sure which specific situation you're referring to, but in general, yes, what you are saying is true. Negatively shifted signals have phases that cancel positively shifted signals, if they are added together.
Thank you so much
You're most welcome. I'm glad the video was helpful.
Dear professor,
I have a time series total electron content (TEC) data calculated from a GPS Signal.
I am studyiny seismo-ionospheric anomalies. If I use fft can I extract any useful information about the frequency of the earthquake? Also how can the phase and psd help here?
Good explanation and so useful for me. Thanks.
Glad it was helpful!
Sir Can you upload video of how the upper and lower sideband are generated in amplitude modulation using graphical method
Thank you.
You're welcome!
This is really good! Thank you.
Glad you like it!
I've seen people drawing images with FT..could you give an explanation about that?
I'm not sure what you mean exactly, sorry. Perhaps these videos might be what you're looking for: "2D Fourier Transform Explained with Examples" th-cam.com/video/3gAZ0U66AEA/w-d-xo.html and "Introduction to Image Processing with 2D Fourier Transform" th-cam.com/video/tlwIWjeuu8U/w-d-xo.html
Sir your way of explanation is excellent. I have question related to the negative amplitude in the Fourier transform plot of Rect function. I mean to say that one portion of the Sinc function goes below the frequency axis..what exactly it means? I know it is something related to the phase information of the present frequencies in the signal, but I have not found a clear explanation on this.. plz make a video on this.
Thanks for the suggestion. I did wonder if anyone would ask me about that, but decided it was too much to try to fit into a single video. I'll make another video to try to explain that aspect. In summary, a negative amplitude is the same as a positive amplitude with a 180 degree phase shift. So if you plot the phase as a function of time, it suddenly jumps from zero to 180 degrees (which might seem odd), however it is important to realise that the amplitude goes to zero at that frequency, so in fact it is better to visualise the phasor on a "real and imaginary" plot, and you'll see that the point tracks through zero, and simply comes out the other side (which gives the phase flip).
when you say "add", you mean convolve in Time Domain and multiply in FT right? cuz x(w)e^something only cancels out the conjugate when you multiply.
Sorry, but you'll have to tell me the time-stamp in the video that you're talking about.
i truly love you.
😎
amazing explanation. Thanks
Glad it was helpful!
Amazing example, so if I understood correctly, usually when we see the graph of a Fourier transform of a function f it's ploted as its absolute value |FT| which makes us lose the information of the phase, so if you plot that same function e^{-jw(T/2)}x(w) WITHOUT the absolute value we would have all the information for the phase? or am I missing something?
Yes, that's right. Although it's not easy to think of how to plot the function (on a single graph) _without_ the absolute value, since it has two parameters (amplitude and phase).
At 11:20 , when ω = π/T , isnt it supposed to be 3/2 π instead of π/2 ?
No, it's -3/2π , which is the same as π/2 (I think you're forgetting the minus sign).
I understand the phase means time delay but when you have a signal e^-t there is phase shift. I am not sure why there phase for this signal even though there is no time delay.
Sorry, you'll have to tell me the time-stamp of when I said that. I'm a bit busy right now to re-watch the whole video sorry.
Short answer "yes" right ?
I thought you could give all the information in a Fourier plot by either using + and - frequency, or by plotting real and imaginary components.. This seems to imply its gotta be both?
Yes. For example, a real signal is always going to have a magnitude spectrum that is symmetric around f=0. So in that case, plotting the + and - frequency only tells you that it is a real signal. It doesn't tell you what the phases of each sinusoidal component are, at each frequency.
Very insightful, thanks. When I look at the 3 diagrams on the left hand side, you have a special denotation at the y-axis. I haven't ever seen that. I just know the normal x(t) denotation and the signal is then e.g. x(t-2) to shift the function 2 units to the right.
Does that mean you can put the whole information of the function into the y-axis denotation?
Thanks
The label of the y-axis should be the function that is plotted. If you plot x(t) then label the axis x(t). If you plot x(t-a), then label the axis x(t-a).
thank you!!
You're welcome!
A great video, thank-you! Is there a reason why you prefer to use j over i?
Good question. Electrical engineers use j for the complex variable because we use i for electric current. It's a pain, I know.
@@iain_explains you learn something new every day!
wao
Glad you liked it!
Fourier transforms is when I realized I don't like math but I do like programming
I think the Fourier Transform of x(t)=rect(t/T) is incorrect.
It's correct. Perhaps you are getting confused with the sinc function? I deliberately didn't write it in terms of the sinc function (as many people do) because there are two different definitions of the sinc function - so it can be confusing.