Please i need a comprehensive tutorial on fourier series. who knows?
here it goes. First understand that a square wave can be decomposed into its fundamental and harmonics. Thus a square wave of 50 hz will ideally contain 100,150,200,250 hz etc, not in same amplitude and phase. Actually because the square wave with 50% duty cycle (10mS On and 10mS off) will have no even harmonis, such as 100 hz, 200 hz etc. It will have odd harmonics whose amplitude is 1/3 for 150 hz, 1/5 for 250 hz, 1/7 for 350 hz and 1/n for nth harmonic with n as always an odd number. And they should not simply be added up. They have to have 180 deg phase shift if (n+1)/2 is an even number. It might take some time before you digest this idea. But try. A sine wave has only one frequency. No harmonics. How to identify whether a wave has harmonics and if so its amplitude and phase? that is what Fourier analysis does. It analyses the wave and identifies the presence of harmonics. In a way of speaking, it multiplies by sine and cos of the harmonics and integrates the product. If the integral of product is zero, then that harmonic is absent. Now read about this in various books. Start with BP lathi. Understand the mathematical operations, and you will find therein expressions for the square wave in terms of the harmonics such as sinwt-sin(3wt) /3+sin(5wt) /5-sin(7wt) /7+etc. The signs indicate alternating 0 and 180 deg for the harmonics that are present. Obviously wt is fundamental, 3wt is third harmonic etc. Download circuit maker and you can generate a square wave from a properly phased set of sinusoids of 50,150,250,350 and so on when you add them, if you take care of their amplitude and phase. perhaps this is what everybody should teach before thay start with the mathematical expressions which goes above the head.