Third order approximation

• The square wave can be approximated by the sum of two sinusoids of frequencies 1 Hz and 3 Hz.
• The aprroximating signal is given by
  
  $$s(t) = \frac{4}{\pi} \sin(2 \pi t) + \frac{4}{3 \pi} \sin(2 \pi 3 t).$$
  
  

• As the figure below shows, the approximation is significantly better than before.
• Not only have the square wave and the approximating sinusoids the same sign.
• Differences are less severe near the transitions of the square wave.

  

Figure 4.3: Approximation of square wave by sum of two sinusoids.