【正文】 0,1,1]。Answer: Define: So: Then: So: It proves that g(t,T) depends only on tT. Consider a system with impulse response as shown in (a). What is the zerostate response excited by the input u(t) shown in (b)? Translation: (a)所示的系統(tǒng)，(b)所示輸入u(t)激勵的零狀 態(tài)響應(yīng)是什么？Answer: Write out the function of g(t) and u(t): then y(t) equals to the convolution integral: If 0=t=1, 0=r=1, 0=tr=1: If 1=t=2: Calculate integral separately: Consider a system described by What are the transfer function and the impulse response of the system?Translation: 考慮如式所描述的系統(tǒng)，它的傳遞函數(shù)和沖激響應(yīng)是什么？Answer: Applying the Laplace transform to system inputoutput equation, supposing that the System is initial relaxed: System transfer function: Impulse response: Let y(t) be the unitstep response of a linear timeinvariant system. Show that the impulseresponse of the system equals dy(t)/dt.Translation: y(t)是線性定常系統(tǒng)的單位階躍響應(yīng)。其中u表示輸入，y表示輸出。因而對具有某種連續(xù)性質(zhì)的系統(tǒng)，可加性導(dǎo)致齊次性。Answer: The system is not linear, so we can linearize it. Suppose: So: = Define state variables as: , , , Then: =+ = Find a state equation to describe the network shown in also its transfer function.Translation: ，以及它的傳遞函數(shù)。0]。說明正反饋系統(tǒng)的單位階躍響應(yīng)，當(dāng)a=1時，(a)所示。理想低通濾波器是因果的嗎？現(xiàn)實世界中有可能構(gòu)造這種濾波器嗎？Answer: Consider two different time: ts and tr, ts tr, the value of g(tstr) denotes the output at time ts, excited by the impulse input at time tr. It indicates that the system output at time ts is dependent on future input at time tr. In other words, the system is not causal. We know that all physical system should be causal, so it is impossible to built the filter in the real world. Consider a system whose input u and output y are related by where a is a fixed constant. The system is called a truncation operator, which chops off the input after time a. Is the system linear? Is it timeinvariant? Is it causal?Translation: 考慮具有如式所示輸入輸出關(guān)系的系統(tǒng)，a是一個確定的常數(shù)。相應(yīng)的輸出表示為y1,y2 和y3。系統(tǒng)可以描述如式所示形式。[N1,D1]=ss2tf(A,B,C,D,1)Which yields: N1