How can a square wave be represented by a sum of sine waves?
Consider a simple telephone conversation: A person (message source) speaks into a telephone receiver (encoder), which converts the sound of the spoken word into an electrical signal. This electrical signal is then transmitted over telephone lines (channel) subject to interference (noise). When the signal reaches the telephone receiver (decoder) at the other end of the line it is converted back into vocal sounds. Finally, the recipient (message receiver) hears the original message.
A square wave, like other periodic functions, can be represented as a sum of sine and cosine waves through the application of the Fourier theorem.12
According to this theorem, any steady-state periodic wave can be decomposed into a series of sinusoidal components, known as a Fourier series, whose frequencies are the fundamental frequency and its harmonics. Each of these components possesses a specific amplitude and phase that, when summed together, reconstruct the original complex waveform.12
In the case of a square wave, the infinite sum consists of the fundamental frequency and its odd harmonics (e.g., 3rd, 5th, 7th). As you add more successive terms in the series, the resulting sum provides an increasingly accurate approximation of the square wave's shape. This mathematical principle is fundamental to Fourier analysis, which is widely applied in fields ranging from acoustics and optics to radio transmission.21