What is Negative Frequency?

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Iain Explains Signals, Systems, and Digital Comms

Iain Explains Signals, Systems, and Digital Comms

Күн бұрын

Пікірлер: 93
@johncgibson4720
@johncgibson4720 3 жыл бұрын
This channel is pure gold. You can get good job positions if you apply this to high end electronic applications.
@iain_explains
@iain_explains 3 жыл бұрын
Thanks for your nice comment. Glad you like the videos.
@sandeeproy4490
@sandeeproy4490 4 жыл бұрын
What a insightful eye opening explanation. Any amount of appreciation is less. Thank you.
@iain_explains
@iain_explains 4 жыл бұрын
Glad you found it helpful.
@faisaldj
@faisaldj 3 жыл бұрын
This guy deserves more subscribers
@_SeaH0rse
@_SeaH0rse 2 жыл бұрын
He really does!
@rakeshpillai9662
@rakeshpillai9662 Жыл бұрын
still does haha
@gamingwithdad5774
@gamingwithdad5774 4 жыл бұрын
Can you please explain what the purpose of graphing a negative frequency with phasors when negative frequencies do not actually exist? What happens when a computation ends up with a negative frequency?
@iain_explains
@iain_explains 4 жыл бұрын
Ah yes, great question. I should have thought to mention something about that in the video. Anyway, one reason shows up when we start to look at sampling, and another good example is when we look at modulating signals onto carrier waveforms. In both of these examples, the "baseband"/"low frequencies" (both positive and negative) get shifted up to higher frequencies. I'm not sure if it clear from that description, but check out these two videos where you'll see that happening: Sampling: kzbin.info/www/bejne/d5TYgqF_jc6NaKM and Modulating: kzbin.info/www/bejne/Y4G6mGBmoJeiodU
@paulmertens5522
@paulmertens5522 3 жыл бұрын
After watching this video I understand how a real-valued cosine can be expressed as the sum of two complex cosines with a positive and negative frequency. However what this video did not clarify to me is why 'negative' frequencies turn up when performing the Fourier transform of a real-valued signal. The fourier transform of a real-valued signal can be computed without encountering negative frequencies by calculating it as series of dot products between the signal and complex cosines of increasing (but never negative!) frequencies. In this case, the entries in the fourier spectrum which are often attributed to negative frequencies can be seen to actually result from aliasing of frequencies above the Nyquist rate. This is actually trivial to do by hand and I find that provides a more intuitive explanation. I'm wondering if there is actually any benefit to referring to negative frequencies at all, and whether 'negative frequencies' are not simply an artifact of a particular algorithmic implementation of the fourier transform?
@iain_explains
@iain_explains 3 жыл бұрын
Yes, you're right, it is possible to write the Fourier transform without needing the concept of negative frequencies, however it is most commonly done in a way that does induce the negative frequency concept - as illustrated at the 1:25min mark of the video.
@mustakimm6
@mustakimm6 4 жыл бұрын
Very good explanation. Thank you very much.
@iain_explains
@iain_explains 4 жыл бұрын
Glad it was helpful!
@joaquinortiz279
@joaquinortiz279 5 жыл бұрын
Very very good straightforward way to explain this 👍🏼
@iain_explains
@iain_explains 5 жыл бұрын
Glad you found it useful.
@martindegourcuff8854
@martindegourcuff8854 5 ай бұрын
Great explanation, thank you!
@iain_explains
@iain_explains 5 ай бұрын
Glad it was helpful!
@velmuruganr9321
@velmuruganr9321 3 жыл бұрын
I'm speechless....please make more such videos
@iain_explains
@iain_explains 3 жыл бұрын
Have you seen the list of videos on my webpage? iaincollings.com Let me know if there are other specific topics you'd like.
@AbuSous2000PR
@AbuSous2000PR 2 жыл бұрын
many thx again...your channel is way under-rated ... you have explained it well while others repeat what is in text books
@iain_explains
@iain_explains 2 жыл бұрын
Thanks for your nice comment. I'm so glad you like the channel.
@gill6335
@gill6335 2 жыл бұрын
very nice video...I am wondering what would make it for the signala to have only +ve spectrum like the IQ signal.
@iain_explains
@iain_explains 2 жыл бұрын
Perhaps you haven't quite understood the points that are being made in the video, sorry. In reality, all signals only have +ve spectrum. There is no "negative" spectrum. No signals oscillate with negative frequencies. It's just that engineers often choose to represent the "negative rotating phases" of a signal by showing its effect as a "negative" frequency.
@onurkrmz9206
@onurkrmz9206 2 жыл бұрын
great explanation, never understood this before. Now everything is in place. thanks a lot
@iain_explains
@iain_explains 2 жыл бұрын
I'm so glad the video helped to clarify things for you.
@SignalProcessingWithPaul
@SignalProcessingWithPaul Жыл бұрын
My video on Phasors has some animations based on these great explanations; cheers. I don't know if I had fully grasped the idea of negative frequency until this video.
@iain_explains
@iain_explains Жыл бұрын
Glad it was helpful!
@dubsy6443
@dubsy6443 3 жыл бұрын
Is it possible for light to redshift into a negative frequency near the event horizon of a black hole?
@iain_explains
@iain_explains 3 жыл бұрын
Sounds fascinating, but you'd have to ask a physicist.
@Crazytesseract
@Crazytesseract 2 жыл бұрын
If I have a fan with blades rotating at 6000 rpm anticlockwise, then suppose we say the angular speed is positive 6000 rpm. If it rotates in the clockwise direction can we say it has an angular speed of negative 6000 rpm? (Frequency +100Hz and -100Hz respectively). Or am I wrong?
@iain_explains
@iain_explains 2 жыл бұрын
Speed/velocity is not the same as Frequency. In your example, "Frequency" is the number of rotations per second. So it's a positive number. It doesn't include the direction of the spin.
@Crazytesseract
@Crazytesseract 2 жыл бұрын
@@iain_explains But the number of cycles per second (Hertz) is also a positive number; does not include direction either. I specifically said angular (rotational) speed. Rotational speed seems to be very similar to frequency. And angular speed is obtained by multiplying by 2π. One rotation is equivalent to one full cycle. One rotation per second should be equivalent to one cycle per second. Why do you say they are not the same?
@iain_explains
@iain_explains 2 жыл бұрын
Speed is measured in distance per unit time (eg. metres/sec), or angle per unit time (eg. radians/sec). Frequency is measured in "number of times something happens" per unit time. They're different things.
@Crazytesseract
@Crazytesseract 2 жыл бұрын
@@iain_explains Sorry, but I still don't get you fully. What about the term, "revolutions per second"? It has got nothing to do with distance, and the angle is always 2*pi radians. We are mainly counting the number of complete revolutions. I think I should have said angular frequency (or rotational frequency) instead of angular speed?
@iain_explains
@iain_explains 2 жыл бұрын
OK, yes, I guess you can say that. Probably even better to say "revolutions per second in a clockwise direction", so you can say counter-clockwise is "negative".
@CarnaticSriram
@CarnaticSriram 3 жыл бұрын
This is an amazing explanation!
@iain_explains
@iain_explains 3 жыл бұрын
Thanks. I'm glad you liked it.
@georgepalafox5967
@georgepalafox5967 Жыл бұрын
Great explanation Sir! Appreciate you taking the time to make these videos. They are extremely helpful!!
@iain_explains
@iain_explains Жыл бұрын
Glad you like them!
@steve_killemall6182
@steve_killemall6182 Жыл бұрын
Thank you professor for the great explanation.
@iain_explains
@iain_explains Жыл бұрын
Glad it was helpful!
@AleksandarDjurovic90
@AleksandarDjurovic90 3 жыл бұрын
Hi Iain. Thank a millions for this video. If I understood correctly, the real signal (our voice for example) does not contain negative frequency, but we will use this concept when we want to represent real signal as a complex number. Example: cos(x) = 1/2*(e^jx + e^-jx)?
@iain_explains
@iain_explains 3 жыл бұрын
Yes, that's right.
@ayseo7998
@ayseo7998 2 жыл бұрын
So it is the interference frequency of the counter wave which would offset the initial wave.
@iain_explains
@iain_explains 2 жыл бұрын
Sorry, I don't know what you mean by "interference frequency". Perhaps this video might help: "How do Complex Numbers relate to Real Signals?" kzbin.info/www/bejne/in26dmZuba-KfdU
@tescoracers1104
@tescoracers1104 2 жыл бұрын
Why didnt you do this with sin ? wouldve been more insightful as to the phase graph relating to the fourier transform.
@iain_explains
@iain_explains 2 жыл бұрын
Sure. But the additional 90 deg aspect would have potentially confused some people, if I hadn't at least done it with cosine first. Then the video would have been longer. I've got another video that covers the phase aspect: "Is Phase important in the Fourier Transform?" kzbin.info/www/bejne/jaqpgGmvd7Zjeck
@jacobvandijk6525
@jacobvandijk6525 4 жыл бұрын
Clear as one's view on a sunny day! Greetings from NL.
@iain_explains
@iain_explains 4 жыл бұрын
Thanks.
@darrenablett4168
@darrenablett4168 4 жыл бұрын
What frequency does negative charge use?
@amahbubul85
@amahbubul85 3 жыл бұрын
Hi Lain, When do we have imajinary part in X(jw)?What kind of signals have that?
@iain_explains
@iain_explains 3 жыл бұрын
One example is sin(w_1 t). This can be written 1/(2j) [ e^(j w_1 t) - e^(-j w_1 t) ], which you can see gives complex valued delta functions at w_1 and -w_1 in the Fourier transform (due to the 1/(2j) term that multiplies both of the complex exponentials). So, actually the only signals that do _not_ have complex valued Fourier transforms, are ones that only contain cos(wt) components (with no phase offsets - since as soon as you include a phase offset, you are getting a sin(wt) component).
@George-jg6ry
@George-jg6ry 4 жыл бұрын
So a negative frequency is a frequency that goes back in time ??
@iain_explains
@iain_explains 4 жыл бұрын
No. Notice that all the plots I drew in the video go forwards in time. In summary, the cos waveform can be constructed from two complex exponential components. One travels in a positive direction around the unit circle (as time increases) at a rate w_0, the other travels in a negative direction around the unit circle (as time increases) also at a rate w_0. On a Frequency plot, we show the positive directions on the right hand side, and the negative directions on the left hand side (which makes it look like a negative frequency). It's really a positive frequency travelling in the negative direction around the unit circle. It might help to watch the video I made on the relationship between complex numbers and the real world: kzbin.info/www/bejne/in26dmZuba-KfdU
@George-jg6ry
@George-jg6ry 4 жыл бұрын
@@iain_explains Great , thank you very much !
@CuongPhamQ
@CuongPhamQ 3 жыл бұрын
Dear Prof. Iain. Thank you so much. Can you explain the difference between NOMA and SDMA?
@iain_explains
@iain_explains 3 жыл бұрын
NOMA separates users in the "code domain", and SDMA separates users in the "spatial domain". You can use them together. For example, you could implement SDMA at a base station, by using sectorized antennas, and then you could implement NOMA in each sector.
@amanuelnigatu4621
@amanuelnigatu4621 Жыл бұрын
Thank you sir
@iain_explains
@iain_explains Жыл бұрын
You're welcome.
@sniper1326
@sniper1326 5 ай бұрын
Damn🔥🔥🔥🔥🔥🔥 what an explanation. Love from India...❤❤❤❤❤❤
@iain_explains
@iain_explains 5 ай бұрын
I'm so glad you liked it.
@sniper1326
@sniper1326 5 ай бұрын
@@iain_explains Once I get a job I will pay you, for helping everyone to make understand these concepts..💕💕
@iain_explains
@iain_explains 5 ай бұрын
That would be very nice. Good luck in your job search.
@llllNEOllllchannel
@llllNEOllllchannel 3 жыл бұрын
So we need negative frequency in order to create conjugated complex number of given complex number so we could just get rid of imaginary part in given number? Is that right?
@iain_explains
@iain_explains 3 жыл бұрын
Yes, it has that effect. Although the aim is not to "get rid" of the imaginary part. The aim is to be able to represent real signals in the general complex baseband form.
@llllNEOllllchannel
@llllNEOllllchannel 3 жыл бұрын
@@iain_explains that is right, so what do we have? We had single vector on positive frequency that represents 1 harmonics with its own amplitude, frequency and phase shift(using vector length and angle). But the problem is that we actually have 2 vectors, representing this harmonic, not only 1. So the second vector has coordinates such as conjugated complex number of the first complex number. The vectors have the same length and the same angle, if we consider clockwise rotating then clockwise angle is positive in that rotating ofc. But at the same time clockwise rotating is negative frequency, that doesn't really have much physical explanation. 2 vectors with equal length and equal angle represent 1 harmonic. So we need negative frequency for completeness of the solution? What do you think? Sorry for bothering you. Thx for the video, helped me a lot)
@iain_explains
@iain_explains 3 жыл бұрын
I think the point is that negative frequency doesn't really exist. There is no physical phenomena that oscillates with a negative number of periods per second. To most people, "frequency" is like temperature measured in Kelvin. There is an absolute zero, and negative just doesn't make sense physically. But when people come across the Fourier Transform for the first time, and see a plot that shows both positive and negative values for frequency, then it can be confusing. However, if you understand that the plot is just part of the representation of a complex exponential, and that the negative portion of the frequency plot simply represents a negative direction of rotation in the complex plane, then it all falls into place. In terms of your question, you may find it helpful to read the Wikipedia page for the Fourier Transform, and go down to the heading: "Sine and cosine transforms". It explains that the FT can be written in terms of Sin and Cosine functions, instead of the complex exponential. Again though, it needs two functions at the same frequency, which is mirrored by the two functions (positive and negative frequency components) in the complex exponential form.
@llllNEOllllchannel
@llllNEOllllchannel 3 жыл бұрын
@@iain_explains ty
@poiuwnwang7109
@poiuwnwang7109 3 жыл бұрын
nicely exlained
@iain_explains
@iain_explains 3 жыл бұрын
Glad it helped
@indycollie6424
@indycollie6424 2 жыл бұрын
Do you think negative frequency could be used to explain gravity?
@AJ-fo3hp
@AJ-fo3hp 3 жыл бұрын
I Have subscribed your channel. Kindly show sin(wt) as you shown for cos(wt)
@iain_explains
@iain_explains 3 жыл бұрын
sin(wt) is the same as cos(wt), except that the points are rotated 90 degrees around the unit circle, due to the 1/j factor in the complex exponential representation of sin. See this video for more details: "How do Complex Numbers relate to Real Signals?" kzbin.info/www/bejne/in26dmZuba-KfdU
@panduwilantara3070
@panduwilantara3070 Жыл бұрын
good
@atpTUBE
@atpTUBE Ай бұрын
Wuh! Thanks sir, I got where the formulation comes from wight now. Logic, not memorization!
@iain_explains
@iain_explains Ай бұрын
I'm glad it makes sense now!
@giziemcbarns
@giziemcbarns 3 жыл бұрын
Aren't all numbers the same?
@suchetanrs4140
@suchetanrs4140 2 жыл бұрын
Beautiful
@iain_explains
@iain_explains 2 жыл бұрын
Thank you! Cheers!
@mohsen865
@mohsen865 2 жыл бұрын
a big like, well done.
@iain_explains
@iain_explains 2 жыл бұрын
Thanks. Glad you liked it.
@ahmetkoraysonal5841
@ahmetkoraysonal5841 4 жыл бұрын
sir,firstly thank you ,you give very good information, but it would be great if you could ask difficult questions about these topics
@furkancolak3702
@furkancolak3702 4 жыл бұрын
I dont think so. Fundamental topics are much more important. His purpose is not to prepare you for exam.
@christopheracob3689
@christopheracob3689 2 жыл бұрын
Hit like, subscribe and click the bell and don't forget to share.... He explains complex stuffs in its simplest way for easy understanding.
@iain_explains
@iain_explains 2 жыл бұрын
Thanks for your recommendation. I'm glad you like the videos.
@jemussi7842
@jemussi7842 3 жыл бұрын
Height pi?
@iain_explains
@iain_explains 3 жыл бұрын
I'm not sure what your question is, sorry. Maybe you're asking why I said "height"? OK, technically, the "height" of a delta function is infinity, but since we can't draw infinite height, traditionally we draw a delta function with a height equal to the area under the delta function, which in this case is pi. For more details of the delta function, see the video: "Delta Function Explained" kzbin.info/www/bejne/oqrVkqSqgrynfc0
@jemussi7842
@jemussi7842 3 жыл бұрын
@@iain_explains Many thanks for your response. Yes it was the pi term that confused me. The problem is me not remembering my uni maths properly. I think mostly we left it out as it is a constant term as this simplifies the look of things. Also I think we referred to the 'weight' of the delta functions rather than 'height'. Sorry should have phrased my question better. Liked and subsribed.
@malingatembo8850
@malingatembo8850 3 жыл бұрын
This is the most insighful explaination
@iain_explains
@iain_explains 3 жыл бұрын
Glad you found it helpful.
@malingatembo8850
@malingatembo8850 3 жыл бұрын
Thank you
@saththiyambharathiyan8175
@saththiyambharathiyan8175 5 ай бұрын
why fourier series does not have negative frequency.....
@iain_explains
@iain_explains 5 ай бұрын
It does. When k is negative, it corresponds to negative frequencies. See: "Fourier Series and Eigen Functions of LTI Systems" kzbin.info/www/bejne/nYPUZH5qj7Z-n5o
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