signal processing of vibration signal

I have one vibration signal with sampling frequency of 1000 Hz i want to do signal processing of that when i did it my amplitude of signal after FFT is not same.

please help

clc;

clear;

close all;

%%Time Domain Plot

vib1=readtimetable("ks.csv","SampleRate",1000);

tiledlayout(3,1)

nexttile

plot(vib1.Time,vib1.Var2)

L=length(vib1.Var2);

N=2^nextpow2(L);

xlabel("Time(s)")

ylabel("Ampl(mm/s^2)")

title("Time domain analysis")

% % FFt

t=vib1.Time;

fs=1000;

delt=seconds(1/fs); %time step

Totaltime=t(end,end);

my_fft=2/N*(fft(vib1.Var2));%FFT of Signal

abs_fft=abs(my_fft); %Absolute value of fft

delf=fs/N; %Frequency Resolution

n2=0:1:N/2-1; %fft results are plotted for N/2 data points

fk=delf*n2;% frequency values

% abs_fft(1:N/2);

nexttile

plot(fk,abs_fft(1:N/2))

[v,p]=findpeaks(abs_fft(1:N/2),fk,'MinPeakHeight',1);

findpeaks(abs_fft(1:N/2),fk,'MinPeakHeight',1)

xlabel("Frequency (Hz)")

ylabel("Ampl(mm/s^2)")

title('Frequency domain analysis')

% % Spectral density

% nexttile

% pspectrum(vib1.Var2,vib1.Time,"spectrogram")

Answer 1

[dpb]

Have gone through this innumerable times -- and the fft doc gives an example of normalizing the one-sided PSD to match the time series amplitude. See the following links and discussion/examples therein --

<how-to-scale-the-frequency-axis-after-performing-fft>

<obtaining-amplitude-values-from-an-fft>

Somewhere there's a very long conversation in which I give a myriad of examples of the effects of sampling rate and time in output resolution of both frequency and amplitude. Real world signals rarely match the sampling rate identically so that the even with a pure tone without noise the total amplitude of a single frequency bin in the FFT/PSD may not match -- the energy is spread across the nearest bins if the bin center doesn't match precisely; hence to get the total energy estimate one must integrate the peak, not just pick the peak magnitude.

[Paul]

Why should the PSD match the time-series amplitude? I can't find anything on the fft doc regarding power spectrum. It does talk about amplitude spectrum, but that's not the same thing.