Spectrum

• The approximation of a signal by a sum of sinusoids is called a Fourier series.
• The Fourier series can be interpreted as providing information about the frequency content of a signal.
• By plotting the amplitude versus the frequency (k) for the Fourier series we can see how much of each sinusoid needs to be inserted to compose the original signal.
• The Fourier series for the square wave is shown below.
• It is evident, that the square wave has strong low frequency components and diminishing high frequency components.
• Nevertheless, the high frequency components are essential for capturing details of the square wave.
• In particular, rapid transitions lead to high frequency componets.

  

Figure 4.5: Fourier series for square wave.