What is Negative Frequency?

Explains the concept of negative frequency that is often plotted in Fourier Transforms.
Related videos: (see: www.iaincolling...)
• How do complex numbers relate to real signals?: • How do Complex Numbers...
• Visualising Complex Numbers with an Example • Visualising Complex Nu...
• Why are Complex Numbers written with Exponentials? • Why are Complex Number...
• Fourier Transform Equation Explained • Fourier Transform Equa...
• Fourier Transform of the cos function: • Fourier Transform of Cos
For a full list of Videos and Summary Sheets, goto: www.iaincolling...
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[@johncgibson4720]

This channel is pure gold. You can get good job positions if you apply this to high end electronic applications.

[@iain_explains]

Thanks for your nice comment. Glad you like the videos.

[@sandeeproy4490]

What a insightful eye opening explanation. Any amount of appreciation is less. Thank you.

[@iain_explains]

Glad you found it helpful.

[@joaquinortiz279]

Very very good straightforward way to explain this 👍🏼

[@iain_explains]

Glad you found it useful.

[@gamingwithdad5774]

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]

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

[@velmuruganr9321]

I'm speechless....please make more such videos

[@iain_explains]

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]

many thx again...your channel is way under-rated ... you have explained it well while others repeat what is in text books

[@iain_explains]

Thanks for your nice comment. I'm so glad you like the channel.

[@mustakimm6]

Very good explanation. Thank you very much.

[@iain_explains]

Glad it was helpful!

[@AleksandarDjurovic90]

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]

Yes, that's right.

[@SignalProcessingWithPaul]

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]

Glad it was helpful!

[@martindegourcuff8854]

Great explanation, thank you!

[@iain_explains]

Glad it was helpful!

[@paulmertens5522]

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]

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.

[@amanuelnigatu4621]

Thank you sir

[@iain_explains]

You're welcome.

[@dubsy6443]

Is it possible for light to redshift into a negative frequency near the event horizon of a black hole?

[@iain_explains]

Sounds fascinating, but you'd have to ask a physicist.

[@ayseo7998]

So it is the interference frequency of the counter wave which would offset the initial wave.

[@iain_explains]

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

[@christopheracob3689]

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]

Thanks for your recommendation. I'm glad you like the videos.

[@suchetanrs4140]

Beautiful

[@iain_explains]

Thank you! Cheers!

[@panduwilantara3070]

good

[@poiuwnwang7109]

nicely exlained

[@iain_explains]

Glad it helped

[@CuongPhamQ]

Dear Prof. Iain. Thank you so much. Can you explain the difference between NOMA and SDMA?

[@iain_explains]

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.

[@darrenablett4168]

What frequency does negative charge use?

[@tescoracers1104]

Why didnt you do this with sin ? wouldve been more insightful as to the phase graph relating to the fourier transform.

[@iain_explains]

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

[@indycollie6424]

Do you think negative frequency could be used to explain gravity?

[@gill6335]

very nice video...I am wondering what would make it for the signala to have only +ve spectrum like the IQ signal.

[@iain_explains]

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.

[@ahmetkoraysonal5841]

sir,firstly thank you ,you give very good information, but it would be great if you could ask difficult questions about these topics

[@furkancolak3702]

I dont think so. Fundamental topics are much more important. His purpose is not to prepare you for exam.

[@mohsen865]

a big like, well done.

[@iain_explains]

Thanks. Glad you liked it.

[@llllNEOllllchannel]

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]

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]

@@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]

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]

@@iain_explains ty

[@amahbubul85]

Hi Lain, When do we have imajinary part in X(jw)?What kind of signals have that?

[@iain_explains]

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).

[@AJ-fo3hp]

I Have subscribed your channel. Kindly show sin(wt) as you shown for cos(wt)

[@iain_explains]

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

[@jemussi7842]

Height pi?

[@iain_explains]

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]

@@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]

This is the most insighful explaination

[@iain_explains]

Glad you found it helpful.

[@malingatembo8850]

Thank you

[@saththiyambharathiyan8175]

why fourier series does not have negative frequency.....

[@iain_explains]

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

[@faisaldj]

This guy deserves more subscribers

[@_SeaH0rse]

He really does!

[@rakeshpillai9662]

still does haha

[@George-jg6ry]

So a negative frequency is a frequency that goes back in time ??

[@iain_explains]

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]

@@iain_explains Great , thank you very much !

[@sniper1326]

Damn🔥🔥🔥🔥🔥🔥 what an explanation. Love from India...❤❤❤❤❤❤

[@iain_explains]

I'm so glad you liked it.

[@sniper1326]

@@iain_explains Once I get a job I will pay you, for helping everyone to make understand these concepts..💕💕

[@iain_explains]

That would be very nice. Good luck in your job search.

[@georgepalafox5967]

Great explanation Sir! Appreciate you taking the time to make these videos. They are extremely helpful!!

[@iain_explains]

Glad you like them!

[@Crazytesseract]

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]

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]

@@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]

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]

@@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]

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".

[@giziemcbarns]

Aren't all numbers the same?

[@onurkrmz9206]

great explanation, never understood this before. Now everything is in place. thanks a lot

[@iain_explains]

I'm so glad the video helped to clarify things for you.

[@jacobvandijk6525]

Clear as one's view on a sunny day! Greetings from NL.

[@iain_explains]

Thanks.

[@steve_killemall6182]

Thank you professor for the great explanation.

[@iain_explains]

Glad it was helpful!

[@CarnaticSriram]

This is an amazing explanation!

[@iain_explains]

Thanks. I'm glad you liked it.