Where are magnitude and phase in the output of the FFT?

The output of the FFT is just a list of complex numbers. But, we are used to seeing the FFT of a signal represented as a graph of magnitude or phase plotted against frequency. In this video, I explain how to convert the output of the FFT into the magnitude and phase graphs we know and love.
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• Where is Frequency in ...
How the Fourier Series Works (Book and Kindle eBook)
www.amazon.com/dp/B0B1BY5H6T
0:00 - Introduction
0:45 - Ident
0:49 - Welcome
1:18 - Pythagoras' Triangles
1:38 - The FFT output list
2:28 - Rotating triangles, sines, and cosines
3:22 - Representing a sinusoid using a triangle - Part 1
3:39 - The difference between magnitude and amplitude
4:42 - Representing a sinusoid using a triangle - Part 2
5:08 - Adding sines and cosines
5:16 - Calculating magnitude and phase, an analogy - Part 1
6:57 - Calculating the magnitude using Pythagoras' Theorem
7:34 - Calculating magnitude and phase, an analogy - Part 2
7:44 - Calculating the phase using the inverse tangent rule
9:22 - Applying what we've learned to the output of the FFT
9:40 - Book a consultation
9:53 - Something strange in the FFT output
10:11 - Challenge
3D Model:
Portrait of the philosopher Pythagoras Geoffrey Marchal
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Licensed under Creative Commons Attribution-NonCommercial license

[@MarkNewmanEducation]

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[@thePavuk]

I just discovered this channel. I love that style of old tv shows that make sense, not that flashy "behold our 4D presentation and effects".

[@derekbenham4374]

I just discovered your videos as I'm preparing for my PhD competency exam in Electrical Engineering. Like you my professor left me with more questions than answers in my signals and systems class. Thank you for your great videos, they're helping it all come together!

[@MarkNewmanEducation]

AMAZING! Thank you so much for writing. I wish you the best of luck in your exam and if I can help you out with any questions you may have, I would be happy to do so. I've just released my 2nd book in a series on the Fourier Transform. The books take readers systematically through all the core concepts of the Fourier Series and Fourier Transform, using the same intuitive approach I use in my videos. I wonder if it might be useful for you. Here is the link howthefouriertransformworks.com/book-launch.html

[@fern132007]

You are simply an amazing teacher. I wish we could clone you and put one of you in every school.

[@A-mt4zy]

This is the best explanation I have found on youtube. Thank you so much.

[@muhammadumair9214]

you insist me to love math❤, while I'm physicist...... what a tremendously explanation 🎉 i had never seen such explanation.... bundle of thanks

[@chateauxdelacasa6721]

had to pause the video just to congratulate you on this great explanation

[@madanjit123]

Great work Mark. This is one of the best video i have ever watched on signal processing. This made my understanding crystal clear. Thnaks.

[@culater]

I love your work. THANK YOU !

[@faustobarbuto]

Great videos, great didactics. You make learning tough concepts fun and enjoyable.

[@MarkNewmanEducation]

I really appreciate that! Thanks. Job done!

[@diegossina]

your video is of great help to understand the best how the image is created in MRI

[@dilex123explorations]

Great video Mark,thanks soo much.You are a blessing .

[@MarkNewmanEducation]

So nice of you

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Mark Newman You are number 1 !!!!!

[@MarkNewmanEducation]

מוטי.. מה נשמע?? איזה כיף שאתה רואה את הסרטונים שלי.

[@andrewthebladethrower8371]

magnificent, not FFT, but explanation. Concept isn’t easy to grasp, I dug deep into complex numbers and number theory, but this video nicely sums it up. Russian translation is amazing too, though I did not need it, but I know the quality of translation, which is great in this case. Спасибо!

[@williamwelmans8648]

An excellent video. Thanks!

[@MarkNewmanEducation]

Glad you liked it! Check out my new video at kzbin.info/www/bejne/qpu8fqOohKlmfas for more tips on the FFT.

[@user-hz4zh5uc2v]

You're awesome. Thanks a lot.

[@ranjanpal7217]

Amazing video..plase make a video on STFT, WT and HHT

[@shubhamvnsingh3036]

This is beautiful!!!

[@MarkNewmanEducation]

Thank you

[@longluo1788]

Thank you, Mark

[@MarkNewmanEducation]

You are very welcome

[@tsehayenegash8394]

If its possible I give you a thousand likes. Please take areal data like temperature and how to calculate amplitude and phase by using FFT in matlab

[@requestforcommentsua7989]

Thanks a lot.

[@anilpokhrel8136]

Nice Explanation. I m still not getting idea on Synthesis part. If some frequency exists in signal but how we can determine when the frequency component started with what phase and when it ended with what phase. How reconstruction works.

[@AliAhmed-tm1jf]

Thanks. Beautiful

[@omitbadgers5664]

Thanks a lot!

[@MarkNewmanEducation]

You're welcome

[@solaokusanya955]

I adore you!!

[@moulinexish]

if the signal is periodic, does the magintude refers to the frequency of the signal? Thanks for the video, very helpful

[@bradzepfan]

Another treasure!!!!

[@MarkNewmanEducation]

Thank you

[@joshuawille4802]

I fuckin love this guy

[@balajipadimi8485]

i implemented the whole procedure above in labview , but i'm getting the hilbert transform of the input signal as a result why?. and by making phase reverse , that is atan(a/b) giving me correct result . why??? please respond

[@balajipadimi8485]

if a signal of sampling rate 1khz decomposed into various sinusoids, then what is the sampling rate or how many samples are there in the decomposed sinusoid? please answer sir

[@CSBenivok]

The result of the FFT - the decomposed signals - aren't sampled. They are a definition of a sinusoid. And since you know the definition you can create as many samples as you like.

[@manuelzambrano3481]

Usualy my fft give values in the order of thousands, while my signals have values around 3. Does this mean that my fft need also be normalized for amplitude or something like that?

[@MarkNewmanEducation]

Yes. It is sometimes useful to normalize the magnitude of the FFT by dividing it by the number of samples. The FFT works by multiplying the signal by a cosine wave at the test frequency, then adding all the results together, then doing the same for a sine wave then repeating all the above for each test frequency. It's all the adding that is giving you the large result.

[@nareshkumar4207]

Because the signal is periodic one.

[@MarkNewmanEducation]

No. Non-periodic signals will also give you this symmetry. Click on the preview of "Next Video" on the end screen. A clue to the answer is there. I'll be spending the next video (which I am currently editing) demonstrating exactly why this happens to ALL signals that the FFT analyses.

[@sammyapsel1443]

A symmetric( magnitude) FFT is the result of a real signal.

[@MarkNewmanEducation]

It is indeed, but one usually sees the kind of symmetry you are talking about with 0Hz as the centre frequency. I'll be covering that in the video after next. The symmetry shown here is around a frequency that is half of the sampling rate. There is another reason for this symmetry that one would not see if we had performed a Fourier Transform on this signal rather than a FAST Fourier Transform. CLUE: The same symmetry as this would appear in a DTFT and a DFT of the signal. Take a look at the preview of the next video for a further clue (click on the link on the end screen to see the preview).