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Unformatted text preview: Sec. 4.3 Fourier Series and Frequency Spectra FOURIER SERIES AND FREQUENCY SPECTRA In this section, we present three examples of Fourier series. These examples lead us to the important concept of the frequency spectra of periodic signals. Then, a table of Fourier series for some common signals is given. J ieffi Fourierseriesofasquare wave Consider the square wave of Figure 4.4. This signal is common in physical systems. For ex- ample, this signal appears in many electronic oscillators as an intermediate step in the gener- ation of a sinusoid. We now calculate the Fourier coefficients of the square wave. Because , , \ | v , o < t < T o l 2 " t r ) : [ - v , T s r z < t < T o ' from (4.23), it follows that 1 6 1 ,r: hl,,-1t1e-ik'otdt = #olo'", u'0"' a' - h rTo lrrr'-'o'* d' . l r . l- [email protected] I lTot2 J- v f '-'o'o'l'o'' re(-iko.r6) [- lo The values at the limits are evaluated as I z o r o , o t l : - ; : r r i a y T s : 2 7 r ....
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- Spring '08
- Fourier Series, sincethe squarewave