ABSTRACT
A Fourier series may be represented not only as a sum of sines and cosines, but as a sum of complex exponentials. The complex exponentials provide a more convenient and compact way of expressing the Fourier series than the trigonometric form. It also allows the magnitude and phase spectra to be easily calculated. This form is widely used by engineers, for example, in circuit theory and control theory. The chapter explains how the trigonometric and exponential forms are equivalent. However, there is another form that is commonly used – one that directly gives the amplitude terms in the frequency spectrum and relates to phasor notation. This form involves the use of complex numbers. It is called the exponential or complex form of a Fourier series.
