September 2008
Beginner
834 pages
37h 13m
English
Content preview from Electric Circuits and Networks
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14.5 SYMMETRY PROPERTIES OF FOURIER TRANSFORMS
There is nothing wrong mathematically inv(t) possessing an imaginary part. However, it will not be a physical waveform then. We deal with physical waveforms in Circuit Theory. Hence, we deal with real functions of time exclusively. The Fourier transform of a real v(t) has many interesting symmetry properties.
Fig. 14.4-10 Waveform and Spectra for Example 14.4-5
14.5.1 Conjugate Symmetry Property
Let v(t) be a real function of t and V(jω) its Fourier transform. Then, V(–jω) = V*(jω). This can be shown as follows:
This implies that Re(V(–jω)) = Re(V(jω)) and Im(V(–jω)) = –Im(jω). It also ...
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