华科奥本海姆讲义二初步.pptVIP

CHAPTER 2 LINEAR TIME-INVARIANT SYSTEMS 2.0 INTRODUCTION LTI systems possesses the superposition(叠加) property. Represent signals as linear combinations of delayed impulses . Convolution sum(卷积和) or convolution integral(卷积积分). linear constant-coefficient difference or differential equations (线性常系数差分或微分方程). 2.1 DISCRETE-TIME SYSTEMS: THE CONVOLUTION SUM The representation of discrete-time signals in terms of unit samples: The Convolution Sum Representation of LTI Systems 2.6 SUMMARY * Unit sample response h[n] : response of the LTI system to the unit sample δ[n]. δ[n] → h[n] Writing any arbitrary input x[n] as: the response y[n] to x[n] is the weighted linear combination of delayed unit sample responses: convolution sum or superposition sum : Representing the convolution operation symbolically as: LTI system is completely characterized by its response to the unit sample --h[n] . k x[k] 0 1 2 k h[-k] -2 0 2 (b) Example 2.1 n x[n] 0 1 2 n h[n] -2 0 2 (a) Consider a LTI system with unit sample response h[n] and input x[n], as illustrated in Figure (a). Calculate the convolution sum (convolution) of these two sequences graphically. Example 2.2 Consider an input x[n] and a unit sample response h[n] given by Determine and plot the output Using the geometric sum formula to evaluate last equation, we have n … … 2 1 y[n] 2.2 CONTINUOUS-TIME LTI SYSTEMS: THE CONVOLUTION INTEGRAL The Representation of Continuous-Time Signals in Terms of Impulses t ┉ ┉ -Δ0Δ2Δ kΔ ┉ x(t) Staircase approximation to a continuous-time signal x(t) Staircase approximation to a continuous-time signal x(t) x(-2 Δ) t -2Δ-Δ x(0) 0 Δ t Δ2Δ x(Δ) t -Δ0 x(-Δ) t as , the summing approaches an integral and is the unit impulse function The Continuous-Time Unit Impulse Response(单位冲激响应) and the Convolution Integral Representation of LTI Systems Give the