[理工] [工數] O.D.E. (和訊號與系統??)

[BLUEBL00D (藍血魂)]

Let H{。}　be a linear time invarient system such

that given an input function x(t) : (D = d/dt)

H{x(t)}= (D^4 + D^3 + D^2 + D + 1)x(t)

(a)Does the system H{。} has an impulse response?

   If yes , find the impulse response ; otherwise

   give your reasons in detail .

(b)Find all the possible real function x(t) such

   that H{x(t)} = sin(t) .

                ∞
(c)Let y(t)  =  Σ  δ(t-k) , where δ(t) is the
             k=-∞

   Dirac delta function.

                       ∞
   Prove that y(t)  =  Σ exp(i*2pi*k*t) in the
                    k=-∞

   sense of distributions.

(d)Use the above result to find all the possible

   real input function x(t) such that H{x(t)}= y(t).





這題c選項看不懂他要幹麻  有人能夠幫忙講解嗎 謝謝

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◆ From: 220.138.18.5
→ doom8199:c 的證明就直接用 Fourier series 展開
→ BLUEBL00D:還有H{x(t)}= y(t) => H{x(t-k)}= y(t-k) 要怎麼用呢?
→ doom8199:不過 in the sense of xxx  不知道是啥意思 OTZ
→ BLUEBL00D:謝謝 這樣我知道他在問啥了
※ 編輯: BLUEBL00D       來自: 220.138.18.5         (03/14 21:04)
→ BLUEBL00D:另外有人要這張的題目來練習嗎  我可以放上來
推 shinyhaung:B大你可以整題解完嗎? 電機和光電都有考 我不會= ="