How to scale the result of the fft (fast Fourier transform) and how does fourier.m work in MATLAB?

Fourier transform (fft) in MATLAB from accelerometer data for acceleration, velocity and position

In this short video, I explain how to import a given txt file with raw data from some accelerometer in MATLAB, how to extract time steps (in the unit s) and the linear acceleration (in the unit m/s²) into a certain direction from the given matrix, and how to plot this time domain data. The velocity (in the unit m/s) and the position (in the unit m) can be calculated from the acceleration by numerical integration using the 'cumtrapz' function from MATLAB. After checking the validity (setting the first time step to zero, and making sure that all time steps are equidistant) and detrending the data (using the 'detrend' function from MATLAB), I show how to calculate the frequency spectrum and the corresponding frequency values using the given 'fourier' function, and how to plot the amplitude spectrum with a logarithmic axes scaling. Finally, I show how the calculate the maximum change of position at a certain frequency from the maximum change of accelaration and velocity directly, and to compare the results with the initial calculation. MATLAB source code of the example: https://cloud.ovgu.de/s/iN85Gqs8MJx7dQm Chapter marks: 0:00 Introduction 0:21 Load the data set 0:53 Plot the time function 2:54 Calculate the velocity and position 5:51 Look at the time function 7:18 Window and detrend the data 11:16 Check for equidistant time steps and set the first time step to zero 12:28 Fourier transform of the position 13:24 Plot and look at the spectrum of the position 16:08 Find the maximum amplitude and corresponding frequency 19:10 Intermediate summary 19:40 Alternative solution from the spectrum of the acceleration 20:32 Plot and look at the spectrum of the acceleration 21:31 Calculate the velocity and position 26:15 Compare the results 26:37 Fourier transform of the velocity 27:58 Summary and discussion 28:55 Final advice