Understanding Power Spectral Density and the Power Spectrum

Learn how to get meaningful information from a fast Fourier transform (FFT). There is a lot of confusion on how to scale an FFT in a way that provides an understanding of the properties of the time-domain signal, which is addressed in this tech talk. Specifically, it covers how to go from an FFT to amplitude, power, and power density and why you may choose one representation over another—and the scenarios in which they are valid.

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[BrianBDouglas]

Hi everyone! Thanks for stopping by. If you have any questions about the video (once it's live) or in general about PSDs leave them here and I'll try to get them answered. Thanks!

[erickappel]

Dear Brian,
As usual, you blew me away!
Thankyou!!!

[scttstnfld]

I see @BrianBDouglas post a video, I watch. Love these Brian!

[nicholaselliott]

I've been ignorantly neglecting some of the nuances here. Working the matlab examples which model this are the only way to get these fixed permanently in my brain and to apply them correctly at work. Thanks!

[vinZukaZ]

I have been waiting for a video like this for ages now! Great overwie of a topic that is not well understood by many (me included)!

[tjmozdzen]

The second half was really helpful. I was trying to figure out how to scale the fft amplitude to get something meaningful and used a gaussian because I know what it is supposed to be when transformed: e^(-ax*x) --> (pi/a)^0.5*e^(-pi*pi*k*k/a), where a=1/(2*sigma_x*sigma_x). my Ts = 1e-12 seconds and sigma was 150e-12 seconds. I was expecting an amplitude of 375e-12, but got 375 instead as an amplitude. I need to multiply my fft by Ts (or divide by Fs). Why that works, I'm not 100% sure, but the second half of your tutorial has given me a hint where to look. Thanks!

[arash]

Hi, thank you so much for your excellent work. Maybe that is my mistake but at 7:20, it seems to be the power of two sided FFT, not one sided; lets forget about one sided and as the arrow on the slide shows, proceed with two sided FFT: you correctly apply power 2 and then to fulfill the definition of power you must multiple by 2 and all the time that is two sided FFT.

[lohsolomon]

Thanks alot for the video, I’ve been struggling until now🙏🏽

[kurtgn]

at 5:00 why have the blue and violet sin() the same argument?

[chencanqian]

Thank you for you great videos! I was wondering why we are interested in power over amplitude? Why squared?

[ninepuchar]

At 5:02, why does the summation sin(.)cos(.) results in tends to ZERO?

[munifzeybek]

Best explanations and proofs so far. Thanks a lot! Waiting for the similar videos from you Brian. Your help is priceless.

[KRSK]

Thanks for the video. My requests are

Please talk about the units also. If it is a vibration signals, how volts are becoming v2/Hz or something like that.

Also please explain about windowing of time series signal. I heard that it is done to avoid signal leakage stuff


Whether twice the maximum frequency as sampling frequency is enough or more is needed?

And how to find maximum frequency..

[neilphilip]

Brilliant exposition of the subject!!!!

[PlanetTrantor]

So, if I have a pulse (not periodic) I should use the PSD, right? Can I calculate an amplitud graphic or is that a wrong idea?

Edited: forgot it, Now I understand. Amplitud is only for periodic signals. Thanks a lot, great video.

[radon]

Hi Brian! Big fan of your videos. Is it possible for you to show an actual application of looking at random vibration data, performing FFT and make conclusions after looking at amplitude vs freq and PSD? Thanks!

[mahditabatabaei]

Thank you for this great video.
If we have a complex signal, what is the difference? For FFT or other frequency domain evaluation, should we just on the real part or the image part? Or we can do it on the complex value?

[khaledsalem]

Rectangular window should be used by calculating the signal in frequency domain using fft. Is it right ?

[joelevi]

this tutorial is great, explained so much things I wanted to know so simple.. thank you sir❤

just one question..
the script graph plot for the power and the PSD looks the same, shouldn't they be different as for PSD we divide by the sampling rate?

[melvinkencana]

thanks for the video, really helps my thesis.
can you explain the relationship spectral density used by choi (1999) to modified variance ratio into automatic variance ratio?Thanks