ABSTRACT
The Fourier series is a representation of a real-periodic function of time. For the Fourier series of f(t) to exist, the Dirichlet conditions must be satisfied. Most functions of practical interest satisfy these conditions. This chapter introduces the definition of the Fourier transform. It discusses several important properties of the Fourier transform of f(t). The chapter presents the use of the Fourier transform in the context of signal analysis and signal processing. It shows that when the independent variable is time and the transformed parameter is frequency, the Fourier series and the Fourier transform lead to some very useful results that have become the basis of digital data acquisition systems and the subsequent manipulation of the acquired data.
