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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:

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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.

Granger Obliviate
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  • 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. – James Arathoon Nov 18 '17 at 12:28
  • Hi! Thanks for your answer. But now how should I calculate the frequencies? – Granger Obliviate Nov 18 '17 at 16:47
  • I've concatenated my comments together to make an answer. – James Arathoon Nov 18 '17 at 20:18

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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.

James Arathoon
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  • I understand it's enough to think in odd harmonics since the function odd. I do understand we can have only those 2 frequencies: they can sum up to that weird sinusoidal function. I also understand how the band-pass filter works. However I don't understand how you get to only 17th and 25th. Where do those values come from? – Granger Obliviate Nov 18 '17 at 21:31
  • Because the band is between 800 and 1000 right? – Granger Obliviate Nov 18 '17 at 21:32
  • Yes that is correct. The other two common types of filter are the high pass filter and the low pass filter. – James Arathoon Nov 18 '17 at 21:38
  • Yes I know, I had two previous exercises where I analysed the response of a high pass filter and low pass to that signal (the high pass filter replicated well the fast variation of the signal because fast variation are associated with higher frequencies and the low pass filter replicated the slow variations for the opposite reason). – Granger Obliviate Nov 18 '17 at 21:46
  • Didn't you mean the 17th and 19th harmonic? – Granger Obliviate Nov 19 '17 at 00:41
  • Yes your right of course. I do make some very odd mistakes. – James Arathoon Nov 19 '17 at 00:55
  • It's ok, thank you very much for your help, it was crucial for me to understand the problem! – Granger Obliviate Nov 19 '17 at 02:11