Continuous-Time Signals
摘要
The first chapter presents the main aspects and definitions associated with continuous-time signals. More precisely, this section defines the fundamental concepts of signal energy and power, which enable the classification of signals into energy and power signals. It also introduces the special categories of even and odd signals, and elaborates on the basic properties of trigonometric, as well as real, imaginary, and complex exponential signals. These elements serve as the essential building blocks for representing any type of signal in the time domain. Then the focus shifts to generalized functions and, more specifically, to a presentation of the impulse (or Dirac delta) function, the step function, and the ramp function, as well as square and triangular pulses and the comb function, which is used in sampling processes. The most important transformations that can be applied to a continuous-time signal (such as time scaling, time reversal, and time shift) are presented, together with the representation of any signal by means of impulse and step functions. The chapter concludes with a description of fundamental signal operations, such as signal addition and multiplication, as well as signal convolution, autocorrelation, and cross-correlation. The chapter also includes some information about signal vector spaces and their properties.