Frequency Analysis of Continuous-Time Signals

This chapter is devoted to the frequency representation of continuous-time signals. We start with the trigonometric and exponential Fourier series of a continuous-time periodic signal. The reader will get familiar with notions of amplitude-, phase- and power density spectra of periodic signals and will learn how to calculate the average power of periodic signals using Parseval’s equality. Then we introduce the Fourier transform (FT) of energy signals, present its properties, and discuss some practical problems. Amplitude-, phase- and energy density spectra are also defined. We show how to use the Plancherel theorem for the calculation of the signal energy and the Wiener-Khintchine theorem for the calculation of the auto-correlation function of energy signals. At last, using a limit approach, the Fourier transform of power signals is defined. For periodic signals, we give relations between the exponential Fourier series and the Fourier transform.