资料分析数字信号处理review of signal and system.pptx

Review of Continuous-timeSignals and Systemsy(t)f(t)h(t)§1.1 IntroductionAny problems about signal analyses and processing may be thought of letting signals trough systems. From f(t) and h(t)，find y(t)，Signal processingFrom f(t) and y(t)，find h(t)，System designFrom y(t) and h(t)，find f(t)，Signal reconstruction§1.1 IntroductionThere are so many different signals and systems that it is impossible to describe them one by one. The best approach is to represent the signal as a combination of some kind of the simplest signals which will pass through the system and produce a response. Combine the responses of all simplest signals, which is the system response for the original signal.This is the basic method to study the signal analyses and processing.§1.2 Continue-time Signals All signals are thought of as a pattern of variations in time and represented as a time function f(t).In the real-world, any signal has a start. Let the start as t=0 that means f(t) = 0 t0Call such signals causal.u(t)u(t- t0)110t0t0tTypical signals and their representationUnit Step u(t) (in our textbook ?(t)) u(t) is basic causal signal, multiply which with any non-causal signal to get causal signal.Typical signals and their representationSinusoidal Asin(ωt+φ) f(t) = Asin(ωt+φ)= Asin(2πft+φ)A - amplitudef - frequency(Hz)ω= 2πf - angular frequency (radians/sec)φ – start phase(radians)Typical signals and their representationsin/cos signals may be represented by complex exponential Euler’s relationTypical signals and their representationSinusoidal is basic periodic signal which is important both in theory and engineering. Sinusoidal is non-causal signal. All of periodic signals are non-causal because they have no start and no end.f (t) = f (t + mT) m=0, ±1, ±2, ···, ±?α 0 decayingα ? 0 growingα = 0 constantTypical signals and their representationExponential f(t) = eαt α is realTypical signals and their representation α is complexα = σ + jωf(t) = Aeαt = Ae(σ + jω)t= Aeσ t cosωt + j Aeσ t