First order approximation

• The square wave can be approximated by a single sinusoid of frequency 1 Hz.
• The best amplitude is given by $A=\frac{4}{\pi}$.
• As the figure below shows, the general shape of the square wave is appoximated but the details are very different.
• The square wave and the approximating sinusoid have the same sign.
• Differences are most severe near the transitions of the square wave.

  

Figure 4.2: Approximation of square wave by sinusoid.