# DFT analysis of a physical signal

what is the reason for the result that has been obtained from the DFT of the signal of these two images. The first image is a DFT analysis of a physical signal u which has a time history shown below sampled at a 1000Hz the second image is the square of the signal u which has a time history shown in the image after the time history of u

• Welcome to DSP.SE! Are the two images of the same DFT? It looks like the first may be a zoomed version of the second. Is that true? – Peter K. May 16 '16 at 13:07
• the images are analysis of two different signals – Maurice Moh May 16 '16 at 13:37
• right i have edited the question hope it is clearer – Maurice Moh May 16 '16 at 13:44

The first DFT plot represents a typical case of Gibbs phenomenon.

Without further information there is not much we can do to answer it. I cannot post comments yet, so for the second image I will post an answer:

If you sample your signal with 1kHz, according to the Nyquist-Shannon theorem, you can only have frequencies of - to 500Hz in your signal or otherwise you will get aliasing and therefore images of the signal at frequency multiples of your sampling rate.

If your signal is at 980Hz and you sample with 1000Hz, the images will show at 1000-980 Hz, 980-1000, 2000-980, 980-2000 and so on. That is the reason you appear to have energy around 20 Hz in your signal. To get the result you want, you either have to increase the sampling frequency by the factor of two or you need to change the signal to contain only an absolute maximum frequency of 500Hz.

Regarding the first image: It looks like those are caused by summing up sines and cosines to create a rectangle as done with the Fourier series. But like said above: Without further information, there's not much to help you there.

• i have edited the question i hope it is clearer now – Maurice Moh May 16 '16 at 14:05
• what do you mean by the images will show at 1000-980Hz, 980-1000, 2000-980, 980-2000 and so on and that is the reason I appear to have energy around 20 Hz in your signal? – Maurice Moh May 16 '16 at 14:08
• Please look at the pictures of the following Wikipedia article regarding to aliasing. The image spectra overlap the original one thus giving you a signal that is not really there. en.wikipedia.org/wiki/Nyquist%E2%80%93Shannon_sampling_theorem – Jan Krüger May 16 '16 at 14:16