The Significance of Negative Frequencies in Spectrum Analysis

In EMC measurements spectra generated by pulsed signals are often measured. To calculate the spectra theoretically, Fourier methods are usually used. The Fourier transform yields a spectrum which contains positive and negative frequencies. The exponential form of the Fourier series also yields a spectrum which contains positive and negative frequencies. However, the trigonometric form of the Fourier series yields a spectrum containing only positive frequencies. Since there seems to be some doubt about the physical interpretation of negative frequencies, the relationship between the double sided spectrum of the exponential Fourier series and the single sided spectrum of the trigonometric Fourier series is shown. The reasoning is then extended to the Fourier transform to show the relationship between the double and single sided spectrum obtained by the Fourier transform. A method of obtaining spectral levels for positive frequencies only using the Fourier transform is shown.