Notes on Digital Signal Processing: Practical Recipes for Design, Analysis and Implementation

Note 60. Complex and Analytic Signals

An understanding of complex and analytic signals is an essential foundation for the development of many advanced signal processing techniques.

A real-valued signal always has a magnitude spectrum that is symmetric about f = 0, as depicted in Figure 60.1(a). Many different digital receiver architectures depend upon the abilities to (1) eliminate either all of the positive-frequency content or all of the negative-frequency content in such a signal’s spectrum, and then (2) shift the surviving spectral band so that it is concentrated around zero frequency, as shown in Figure 60.1(c). A continuous-time signal having a spectrum that is zero-valued for all negative frequencies, as in Figure 60.1(b), is called an ...