ABSTRACT
It is sometimes possible to predict the harmonic content of a waveform on inspection of particular waveform characteristics.
If a periodic waveform is such that the area above the horizontal axis is equal to the area below then the mean value is zero. Hence a0 = 0 (see Figure 171.1(a)). https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/fig171_1.tif"/>
An even function is symmetrical about the vertical axis and contains no sine terms (see Figure 171.1(b)).
An odd function is symmetrical about the origin and contains no cosine terms (see Figure 171.1(c)).
f ( x ) = f ( x + π ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/eq6155.tif"/> represents a waveform which repeats after half a cycle and only even harmonics are present (see Figure 171.1(d)).
f ( x ) = − f ( x + π ) https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780429294402/968186b9-ffa4-4f2b-aa54-7fc58a604561/content/eq6156.tif"/> represents a waveform for which the positive and negative cycles are identical in shape and only odd harmonics are present (see Figure 171.1(e)).
