So let's say that I have a signal of fundamental frequency 50Hz. I then have a band-pass filter that passes the band between 800 and 1000 Hz of my signal. I don't know the expression of the signals I just know the graphics:
My question now is how should I determine the frequency of the sinusoids that have resulted by processing the signal. I know they might be related with the frequency of the original signal but I'm not sure. Can anybody help me? Thanks.
The blue input signal to your band-pass filter appears to be a square wave added to sine wave (exactly phase aligned in an unlikely way). The sine wave will not pass through the filter so you are just left studying the components of the square wave signal that will.
Square waves can built up of odd harmonics using Fourier series. There is plenty of information on the web (for example http://mathworld.wolfram.com/FourierSeriesSquareWave.html ) giving you the relative amplitude of the odd harmonics.
To read about bandpass filters start with https://en.wikipedia.org/wiki/Band-pass_filter . The simplest assumption is that the bandpass filter multiplies frequencies outside the band by 0 and frequencies inside the band by 1; in that case the 17th to the 19th harmonics of the square wave will pass through unaffected, with all other frequencies completely suppressed. Alternatively you could search out a realistic bandpass filter function and multiply your square wave harmonics using that instead.