The dominant application of the discrete Fourier transform is for performing spectral analysis – analyzing the frequency content of signals. The discrete Fourier transform is often used to approximate the Fourier transform of a signal. In this lesson you will learn the three types of approximations involved in using the discrete Fourier transform to represent the Fourier transform. You will also learn the impact of each of these approximations on the discrete Fourier transform representation of the Fourier transform. Understanding these effects is critical for properly using the discrete Fourier transform to perform spectral analysis and interpreting the result.