In this chapter we will examine the Fourier transform for continuous and then discrete signals, the creation of spectra, and dynamic spectra or windowed Fourier spectra and then wavelet transformations a more recent development. Fourier Transformation A signal is a function that conveys information, generally about the state or behavior of a physical system. Continuous-time signals are defined at a continuum of times and thus are represented by continuous time variable functions. We usually refer to signals that are continuous in time and amplitude as analog signals. Discrete-time signals are defined at specific moments in time and thus the independent variable takes on only discrete values.
Digital signals are discrete in both time and amplitude.
The eigenvectors of linear time-invariant systems are complex sinusoidal waves, e i t . This process is known as Fourier analysis. The Fourier transform provides a spectral density distribution which identifies the amplitudes and phases at the various frequencies that contribute to time series. However, it provides no information on their temporal or spatial localization within the time series. The bottom two panels show that the transform of a constant signal is a delta function and vice versa.