In this chapter, the discrete Fourier transform (DFT) will be discussed. The Fourier transform discussed in the previous chapter is quite useful, but the applications will be limited for two reasons. First, the function in the time domain must be representable in closed form so that the Fourier integral can be performed. Thus, unless the input function can be written in closed form, it is impossible to evaluate the integral. Second, even if the time function can be written in closed form, it might also be difficult to find a closed-form solution to the integral.