Spectral Analysis using the FFT

To begin this discussion on spectral analysis, let us begin b y considering the question of trying to detect an underlying sinusoidal signal component that is buried in noise. Such problems occur, for example, very commonly in the area of telecommunications. Suppose that su ch a signal-in-noise situation gives rise to the observed data record as shown in figure 1. Here the samples are collected at a spacing of ∆ = 0.1 second apart, and are contained in a MATLAB vectorx so that since the samples are plotted with the command