The Fourier Transform- Part III

[erjavedshaikh]

awooooooooooosome all three videos were really helpful. Thank you sooo much

[adastra123]

What a talented teacher. I get it !!!!!!!!!! after years of not getting the whole picture , I finally get it !!!!!!!!!!!!!. Thanks a million , I feel confident about all that stuff now . You are worth a thousand shrinks when it comes embuing to self confidence. I am going to have a banana now to celebrate. Thanks for those videos , you are a gifted teacher , thanks so much.

[SnatThatBat]

I logged in just so I could like this. "Think of it as an algorithm." changed my life

[seniorbooboojuice1]

Thank you so much sir! I learned what the Fourier Transform really is from you! I'm grateful

[GarbageDevon]

Thank you so much for posting this! I really learned a lot.

[Zanneth]

These videos really helped a lot, thanks!

[igormon]

Do you have any videos on signal sampling and quantization? I couldn't find any in your channel.

By the way your video was very helpful.

[rudymanuel]

thanks so much ...its a very good video , i see that you use matlap to help understand the waves in real and unreal , i speak spanish , but the way you do that is exelent , I'm studing electric engineering , and it help me a lot !!!

[Arlesterc]

Good video on a difficult topic. However I got lost at about 2:28. I am not sure what the multiplication is that makes the sine term disappear in the top diagram. It seems that the multiplication would be {3sin (3Hz) +.8cos(8Hz)}*cos(wt)(3Hz) which works out when distributed to be {3sin (3Hz)*cos(wt)(3Hz)} +.8cos(8Hz)*cos(wt)(3Hz). It seems that first term here goes go 0 - I don't get it. Perhaps an example with actual numbers might help me. Any time taken to respond is appreciated in advance.

[yngwievanhendrix]

This was the best explanation of FT ever.

[teja722]

at 3:53

you multiplied cos omega t with signal at time 0.2 , and resultant shaded green is +ve curve How so ?

[Exploratorius12]

could it be that you forgot a minus sign in the exponent of the e-function? then you'd also have to subtract the imaginary sin integral instead of adding it. anyways thank you for this informative video.

[eksman187]

like ya explaination

[LANN98]

del t is the upside down triangle, not delta t.

what programs did you use for this?

could you also say that the frequency of a graph is the difference of the reference point from the curve, since we are looking at the point at which the curve crosses the nodes of the reference?

[engineer0555]

excellent explanation i can say

[kridnix]

Yes, the magnitude-phase is actually the more common way to represent the signal since it can be hard to tie real-imaginary representations to actual physically measurable variables, at least in my field.

[Cerberus204498]

Very comprehensive vids, congratulations. Two questions I would have for you: what the magnitude formula equals to? Is the magnitude-phase plot the envelope for the other frequency domain signal represention?

[tallycraigslisting]

Awesome video, thanks alot! I signed up for youtube just to say thanks!

[tdr5000]

what exactly are you multiplying at block 4 (multiply by delta t)? Is is the sample rate? so if you were taking 1khz samples, delta t would be 1?

Thanks in advance

[qubei]

Thank you! Explained it perfectly for me. Wanted to understand this for many years.

[iBradleyAllen]

at the end there, the phase of the last signal was a sawtooth wave, but why? and i didnt get why at the 8:00 mark the phase?

Today the FT made sense. finally! i was reading about it, the mystery was solved, you multiply in different frequencies, whatever resonates stands out. i knew for years it was a process of multiplying a set of samples; your video helped clarify this;

[jozet77]

nice explication, thank you

[abuddy4uin06]

thx a lot.. its like i hav understood so much tat i cud nt grab in ma past 1 yr...

[protikmaitra]

The very last slide (9:10) looked like a Gabor Filter.

Q1. I was wondering how I could make a Fourier Transform or Gabor Filter Response more robust by exploring different phases. Is it necessary? Could you please recommend some short cuts that are fast? The only option right now for me is to code it out.

Q2. What if the input signal is sinusoidal but entirely positive?

Q3. What is the frequency if the spikes in the real and imaginary parts (8:16) do not coincide? Is it possible?

-Thanks-

[kridnix]

@protikmaitra For Q#1 I have no idea since I am not a signals guy. I would try to code this up using some sort of genetic algorithm but that is just me not knowing this area. Q#2: This is a sine wave plus a DC component. Since the FT is linear it is a delta function in frequency plus a large spike at frequency zero that is meaningless. Q#3: I believe they need to coincide or else the signal isn't causal. You can manipulate numbers to create signals that couldn't exist in physical systems

[protikmaitra]

@kridnix Thanks for responding.

That made it pretty clear.

Actually, I am trying to use FFT, PSD, Gabor etc., to detect images (image processing and machine learning).

Recently I got some good results using some of the FFT concepts and a binary classifier.

Many thanks for uploading these videos.

-Regards-

[metabog]

Very good explanation, it makes it easy to see exactly how it works.

I swear the first time you hear about it and what it does, it sounds like magic.

[beskhu]

thank you very much this is the best explanation i've ever seen on the fft.

[extremedavo1979]

This was a purely mathematical explaination of the algorithm. He does not explain all the implicaitons of Fourier analysis in a practical signal analysis sense i.e. nyquist, sampling etc.

[kridnix]

@extremedavo1979 That is absolutely correct. In less then 30 minutes I would have a hard time explaining the practical implications of the Fourier Transform in a way that was more than a brief overview.

[naturespark2015]

Thank you so much, kridnix! This video helps me a great lot in understanding FFT! I can't waite to watch your other videos now! Thank you!

[kridnix]

If you want to write software check out "Numerical Recipes in X" where X is either C, C++, or Fortran

[johanhendriks]

nice video, very helpful. i think i might be able to program some interesting software now :)

[boshank20]

Very well explained. The graphs and examples help a lot. Keep up the good work!

[waqsohwaqso]

thanks alot 

[IronPump89]

Thanks alot man, but why is there an imaginary term. If it is a complex number you have to find it length right? I mean you always have to calcualte the absolute value of the vector using the pythagorean theorem....

[mortenrobinson]

@IronPump89 You're absolutely right , to find the amplitude of the wave represented by a complex number you measure the magnitude or length of the cmplex vector, however you also need to know the frequency of the waveform which is equal to the angle that the complex vector makes with the x axis or real-axis. Complex numbers or solemnly used because of their abillity to contain 2 values, or 2 pieces of information if you will, within a single number.

[yashimato]

Thank you so much!!!

[WaqasKhan411]

Thanks alot kridnix for posting these 3 videos they helped me alot in understanding a scary thing like fourier transform

[ryeryeeect]

My head hurts after watching these three videos. Is this what it means to learn something. After all my time in college I am confused, I have never felt this sensation before. :D

Thank you for the video's they are greatly appreciated, its nice to see educators who go above and beyond only for the sake of educating.

[kridnix]

@ryeryeeect Yep, that is what it means to learn something. If you understand it you will never forget it. If you forget it, you didn't understand it.

[Mrknightrider777]

@kridnix again the summation does not mean that we add all the values of function, due to delta function we have only one value at a time.thanks

[captaineggman]

@ryeryeeect I hear ya, it's a good hurt

[jmpuentez]

@ 3:28 did you mean to say there is no COSINE component???

[sweFredro]

This helped me a lot, doing visuals is a great help. I hope our teachers could use the same method

[CongWW]

u legend!

[50millANDaSuit]

this is amazing! i understood! thanx man!!!

[emefear]

it really helps..thanks kridnix..

[chipsmet]

This is a question for anyone willing to assist my understanding:

If the amplitude values for the initial (unknown) function were extremely large, say large enough that it caused problems with using computer integration. Can you modify the original function's amplitude by (1/x), and determine the signals? Then multiply the solved Fourier function by 'x' to get the real-world function?

[kridnix]

@chipsmet Yes. Remember that for any integral you can pull constants outside the integral sign and multiply the result of the integration by the constant at the end. The Fourier Transform is basically an integral, so this is legitimate.

[chipsmet]

@kridnix Thank you kridnix, I appreciate your posting this tutorial and your response. I have a follow up if you don't mind. The example shown here presented a case where all signals were initialized at t=0. In a computer model it is simple to check for phase shifts. If each frequency was found to have unique phase shifts, the integration over any range is still valid, correct?

[kridnix]

@chipsmet Yes. Remember the time shift theorem of Fourier Transforms allows you to shift a signal in time by an amount tau and the corresponding FT is simply multiplied by a signal exp(i*omega*tau) which is a frequency dependent phase shift. So it doesn't matter when a signal "starts" it just has a phase shift in the frequency domain.

[RadioScarecrow]

Very helpful! thankyou.

[rcaccese]

AH! Now I think I get it. Waves (such as radio waves) have both amplitude and phase which coexists simultaneously. Even though the amplitude goes to zero, the signal still exists and has a phase. Radio frequencies have a magnetic component which is 90 degress to the radio wave and has a 90 degree phase difference as they travel through space. So a wave is a 3 dimensional object and the components of amplitude and phase describe the wave.

[kridnix]

@rcaccese Yep, that is it. Very hard to visualize, but the energy of the wave has to go somewhere. When the electric field is zero the magnetic field is a maximum and v.v. Once you get the idea that waves carry energy, and the energy can't just disappear at certain times it makes more sense.

[kridnix]

Good question but hard to answer simply, partly because my own mental picture relies on mathematics. A wave has two numbers that define it- amplitude and phase. The amplitude is how tall the peaks are and the phase is where you are on the wave. At some points in time (phase) the signal will be zero even if the amplitude is large. The real part is the amplitude you can measure and the imaginary part is where the amplitude goes when the signal is less than the amplitude of the wave.

[rcaccese]

Basic question. Can you explain a little about the difference between the real (cos) and imaginary (sin) parts and why they are called real and imaginary?

[RadioScarecrow]

@rcaccese The coefficient of the sin part contains j, the square root of -1, which is undefined in real numbers.

[ylloree]

nice videos... fourier is easy if it can be explained the way you do... keep em coming... more power to you...

[BENLADEN7th]

Really Nice Series

But I have a small question .. Is there is anyway makes you know whether the integral will be =0 grater or smaller ??

Or I need to plot it??

Thanks Again ..... You made the Fourier Simpler :)

[kridnix]

@BENLADEN7th You have to do the integral. IF it is solvable analytically you simply plug numeric values into the solution. Most of the time you solve it numerically using the Blackman-Tukey algorithm or some variant and calculate the value that way.

[BENLADEN7th]

@kridnix Thanks

[samlyonfr]

thanks! i find it very pedagogic, thanks really.

[BAJANCHAMELEON]

BRILLIANT!!!!Thinking of using this for detonation dectection.

[sjIndiarocks]

Thank you very much ..It helped me understand the messy fourier trans...

[hummosa]

Eternally grateful to you! You rock!

[nanaa0]

Hi,

Thank you for this wonderful demonstration. Never seen such a good video before. May I ask whether you could kindly do similar videos for digital filters and wavelet filters. Thanks in advance

[lelugodruid]

Great video :D I know how to do the Fourier transform but I could never understand what was the real meaning of it. I used to panic because I didn't understand what it was about. This video made me enjoy Fourier transforms. Thx :D

[xzeenko]

Awesome explanation. Much much better than how my professor taught it. Thanks for taking the time to put these videos together!

[threefourthreeguilty]

"Hopefully you'll understand Fourier transforms a little bit better"... You couldn't have made it any more crystal clear! Thanks so much!

[chansonjoy]

I'v been tortured by my DSP professor about this formula for long time. now I relieve.

[kulminaator]

nice sum up :)

[dilish1]

really awesome......simple and informative....

[kerrs4]

NOW I GET IT! Can you lecture at my university please?!!!

[kridnix]

Hey, I am always open to new job offers. Ask your department head, but with this economy not many places are hiring :->

[saltydog78]

Hello. I have a question on the wave equation for an infinite string using the Fourier Transform

utt = uxx , - inf. < x < inf.

u(x,0) = 1/(x^2 + 9)

ut(x,0) = exp(-x^2)

Why is that the solution has an integral with substituted boundary conditions?

[kridnix]

This sounds like an attempt to get help on a homework problem... If you can tell me where I can buy an infinite string I'll think about helping you.

[saltydog78]

You can connect the two ends of the string yielding it infinite...Just kidding. Yeah I finally figured out the problem, but a heavy price has been paid by doing so; namely starvation and sleep deprivation. I'll be subscribing to your videos..Thanks Dr.!

[pepomk123]

Brilliant.

[vermixtube]

very nice ...thanks a lot .

[IronPump89]

thanks dude, I finally understood it.

your awesome

[metabog]

Thanks a lot man!

[psyauto]

Thank you mate!

I understood at last!

And yes im a visual learner too!

cheers! ^_^

[BlackJavaBean]

THANK YOU! I absolutely hated Fourier Transforms in my Signals class - I was inundated with math and theory but the prof. never really broke it down like that. I'm kinda visual so seeing it in this form really helps me - just wish I had found this during that class. AWESOME explanation!

[kridnix]

Thanks for the encouragement. We know that engineering students are visual learners, but us faculty aren't taught how to support this type of learning. Hopefully things will slowly change!

[dazzlepecs]

good stuff man. And ive watched a lot of tutorials today... This vid deserves more viewers!!

[proyabun]

thanks. you are awesome.

[TheWye]

Excellent.. Thanks!!

[funky2flavor]

thank you! that really helped...!

peace!

[Alveuz]

as everybody says here, this video rulez! this was very educational :D

[abdulbabam]

After ı watched these videos, I can understand the what the logic of Fourier transform is. Thank you so much for best videos. I hope you upload the new videos presented the matlab codes and the videos also presents the explanation of matlab codes and so on.

[hunor6]

Very good video, thanks for making such things :)

[ruthere1234]

One of the best explanations about FT. Thanx.

[ee04395]

thank you

[mullened]

Thanks alot, it is great presentation

but is this the end of tutorial for Fourier transform?

[whoknowssunshine]

i must say thank you to you. This is a great tutorial.

[javad101]

a great video,

[fredddy1986]

Great video thanks!!

[neantibi]

thank you

[kridnix]

That is a good question. Basically every signal has some bandwidth defined by how precisely the signal needs to be recreated. Generally speaking you don't want to extend the algorithm beyond the bandwidth of the signal.

[bvarvind]

so I guess a TD signal could have many waves @ diff frequency and I am wondering when I should stop substituting the freq value.what is the end condition for the algorithm

[photon100b]

Thanks for the giving invaluable insight in FT.

[trystanlea]

Thanks for the explanation, it helps a lot.

[manf1234]

Thank you very much, I like the way you explain it. It is in fact simple but it needs such a good explanation.

[zuojianqiu]

Thanks for sheding light on Fourier transform with unconventional apects.