Fourier series square wave

​A square wave might look boxy, but Fourier analysis proves it's actually built from an infinite stack of smooth, curvy sine waves.
​Here are the three golden rules of a square wave's Fourier series:
​Only Odd Harmonics: A true square wave contains the fundamental frequency and only odd multiples (3rd, 5th, 7th, etc.). There are zero even harmonics.

​Sine Waves Only: If the wave is perfectly centered on the x-axis and crosses zero at t=0, it is constructed entirely of sine waves (no cosine terms).

Fading Amplitudes: The higher the frequency, the smaller the wave. The amplitude of each harmonic shrinks proportionally to 1/n (e.g., the 3rd harmonic is exactly 1/3 the amplitude of the fundamental).

The Equation
​For an ideal square wave with amplitude A and fundamental frequency \omega_0, the Fourier series is:
f(t) = (4/pi) * [ sin(wt) + (1/3)sin(3wt) + (1/5)sin(5wt) + ... ]

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