信号与线性系统信号与系统.PPTVIP

CHAPTER 1 Signals and Systems 1. Signals1.1 Definition and Mathematical Representation of Signals Signals: physical phenomena or physical quantities, which change with time or space. Functions of one or more independent variables. example: x(t) 1.2 CLASSIFICATION OF SIGNALS 1.2.1.??Continuous-time and Discrete-time Signals （连续时间和离散时间信号） continuous-time signals’ independent variable is continuous : x(t) discrete-time signals are defined only at discrete times : x[n] Representing Signals Graphically 1.2.2 Periodic and Aperiodic Signals （周期和非周期信号） For a continuous-time signal x(t) x(t) = x(t + T) for all values of t. For a discrete-time signal x[n] x[n] = x[n + N] for all values of n. In this case, we say that x(t)(x[n] ) is periodic with period T(N). Example 1.1 Determine the fundamental period of the signal x(t) = 2cos(10πt+1)-sin(4πt-1). From trigonometry, we know that the fundamental period of cos(10πt+1) is T1=1/5, and sin(4πt-1) is T2=1/2. What about the fundamental period of x(t)? The answer is if there is a rational T, and it is the lowest common multiple（最小公倍数） of T1 and T2, then we say that x(t) is periodic with fundamental period T, or else, x(t) is aperiodic. For the x(t) in this example, the lowest common multiple of 0.2 and 0.5 is unit 1, and it is rational, so that the fundamental period of x(t) is 1.  1.2.3 Determinate and Random Signals （确定性信号和随机信号） A determinate signal ——x(t) A random signal —— cannot find a function to represent it The time-average power over an infinite interval:  With these definitions, we can identify three important classes of signals: Energy signals Power signals Signals with neither finite total energy nor finite average power 1.3 Transformations of the Independent Variable of Signals time shift（时移）: x(t-t0) or x[n-n0] time revers