How to scale FFT and PSD in Matlab

[@humantribemember]

I enjoyed watching this as I needed to refresh. What I loved, is that the explanation really added meaning to the math. If you cant explain it in plain language then it hasn't been understood and David knows his subject!

[@byungjinkim6569]

what is Y in the code?

[@kaxxamhinna5044]

Thank you so much 🎉 you saved my day with this video. Have a great day.

[@danielLittle11]

If I’m not mistaken, when you divide by the total time, you are no longer plotting the power spectral density, but rather just the power spectrum. The density is the power PER bin, and the power spectrum is the power distribution of the signal as a function of frequency. The reason I’m saying this also, is that dividing by the total time changes your units of what you are plotting. PSD can’t equal PSD/T. They have to be two different things

[@davidricketts7975]

Before you divide by T, you have energy, which is proportional to how long the measurement is. By dividing it by time, you get the power density. If I mention “PSD” before I divide by T, then that would have been a mistake, it should be energy.

[@arathip7792]

Dear sir, I have a doubt. Insted of 1/ fs * N Can we use fs/N . That is frequency bin width. After taking fft how will choose scaling factor. Which scaling factor will choose for calculation of PSD. 1/fs*N or normalization by fs/N? Pls reply sir.

[@gat0tsu]

thanks alot for the explanation this was extremely helpful

[@helmutalexanderrubiowilson6835]

very clear explanation

[@GiovanniMantovani-tx6oq]

Thank you for the amazing video even after 4 years! I only have a question if you don't mind: around 12:07 min, you convert the Normalized PSD to que correct amplitude of the signal. How did you end up with 0.25 = (0.7/sqrt(2))^2? I mean, why the sqrt(2) came up? Thank you so much again!

[@hgl9590]

the power of a sine wave is A^2/2, where A is its amplitude.

[@tarihad1145]

Thanks for the video. How did you ge the power spectrum is calculated as (V/sqrt(2))^2

[@vigneshkumar7581]

Professor! Thanks for a nice video. Can you please explain how energy_t and energy_f is calculated?

[@memecan2000]

energy_t=sum(abs(x).^2)/length(x) energy_f = sum(abs(fft(x)).^2)/(1/(Fs*length(x)) or something like that

[@balintfurdek552]

Thank you Sir ! Great explanation !

[@mohamadhamoudy8232]

Dear Professor David S. Ricketts , thanks a lot for this valuable video . Please Parseval's Theorem mentioned here is used to compute total Energy in discrete time sequence so why did you use dt to approximate the energy of the signal as if it where a continuous time signal ? Also to plot the single sided magnitude spectrum why we have to divide by L in the , why matlab computes the DFT coefficients multiplied by scaling factor ? Thanks

[@RobertoGonzalez-qd5ri]

Thank you for the explanation! Could it be possible to see the rest of the code?

[@tsehayenegash8394]

I have 15 years temperature data in excell. How can I draw using periodogram?

[@danielLittle11]

I'm coming back to this because I can't seem to figure out how you're integrating your time signal and your frequency signal and getting the same values. I'm using something like "E_Signal = sum(p.^2)/N" and "E_PSD = sum(psd.^2)/N^2". Is this close to what I should be doing? I'm getting drastically different answers

[@chandrakommineni5800]

I'm having same doubt, if it is PSD the units should be v^2/HZ. check out the paper ''Tutorial on Scaling of the Discrete Fourier Transform and the Implied Physical Units of the Spectra of Time-Discrete Signals" . I don't know, I'm still confused