EE5410 Calculating the impulse response h[n]

EE5410 Calculating the impulse response h[n]

excerpted from : Joyce Van de Vegte : Fundamentals of Digital Signal Processing. page. 123-125

eg. 4.11. Find the first six sample of the impulse response for the differece equation :

y[n] - 0.4y[n-1] = x[n]-x[n-1]

1. First replace x[n] with delta[n] and y[n] with h[n] to give:

h[n] - 0.4h[n-1] = delta[n] - delta[n-1]
or
h[n] = 0.4h[n-1] + delta[n] - delta[n-1]

2. Starting with n =0: therefore,

h[0] = 0.4h[-1] + delta[0] - delta[-1]

The values for the impulse function delta[n] are known: at n=0, it has the value 1, and at all other values of n, it has the value 0.

3. The filter can be assumed tobe casual, which means that the impulse response is zero BEFORE n = 0. Therefore,

h[0] = 0.4(0.0) + 1.0 -0.0 = 1.0

Notice that delta[-1] =0 because zero is the value of the function delta[n] when n= -1, not a consequence of causality.

4 The subsequent impulse response samples are :

h[1] = 0.4h[0] + delta[1] -delta[0] = 0.4(1.0)+0.0-1.0 = -0.6

h[2] = 0.4h[1] + delta[2] - delta[1] = 0.4(-0.6) +0.0-0.0 = -0.24

h[3] = 0.4h[2] + delta[3] -delta[2] = 0.4(-0.24) +0.0- 0.0 = -0.096

h[4] = 0.4h[3] + delta[4] - delta[3] = 0.4(-0.096) +0.0- 0.0 = -0.0384

h[5] = 0.4h[4] + delat[5] -delta[4] = 0.4(-0.0384) + 0.0- 0.0 = -0.01536

存在主義神學的內容 :

存在主義神學有表現兩種型態，第一種表現在強調形上學（或 稱為本體論 ）的學說，該學說主張：

上帝是落在現象世界以外的位格，並且人類的認知能力僅僅止於存在著的這個現象世界，換言之，上帝是人類不可能認識的對象 ── 祂永遠不會成為人類認識活動的客體。

這宇宙若有一位造物主，祂就必定會是一位「 永遠的主體」，倘若上帝與受造物並存於這個世界並且淪為人類觀察的對象，那麼這一位就必然不是上帝。

這一種存在主義神學 有它明顯的古希臘哲學淵源，尤其是新柏拉圖主義 透過奧古斯都影響基督教而完成的教父時期神學。

第二種 存在主義神學的表現在於強調我們應該同情「生而為人」這種無可施為之處境上。簡單說這就是經祁克果 與尼采 再提出以後影響歐洲哲學的存在主義之精神內容。