## Montag, 13. Juni 2011

### EE5410 Signal processing --Properties of the sinc() function

EE5410 Signal processing --Properties of the sinc() function

1. The value at w=0 is X(j0) = T. When we attempt to evaluate the sinc formula at w=0, we obtain the indeterminate form 0/0. However, using L'Hopital 's rule from calculus, we get X(j0) =T. Note that we could also use the small angle approximation for the sine function ( sin(x) ~x ) to obtain the same result.

2. The zeros ( at x(t) = 0 ) of the sinc function are at nonzero integer multiples of w = 2PI/T, where T is the total duration of the pulse.

Note that the sinc function oscillates between positive and negative values.

Specifically, it crosses zero at regular intervals because we have the function sin(wT/2) in the numerator.

The zeros of the sinc function are the values of w where the numerator of X(jw) becomes zero. These are the values of w such that sin(wT/2) =0.

Since sin(x)=0 for x =n*PI where n is an integer, it follows that X(jw) =0 for wT/2 = n*PI or w = (2*PI/T)n.

3. because of the w in the denominator of X(jw), the function "dies out " with increasing w, but only as fast as 1/w.

4. X(jw) is an even function : i.e., X(jw) = X(-jw). Thus the real even-symmetric rectangular pulse has a real even-symmetric Fourier transform.

http://molihuaxingdong.blogspot.com/2011/06/blog-post_1371.html

6月8日凌晨，鄭州市公安局治安大隊與經偵大隊辦公院內發生爆炸。5月26日，江西省撫州市發生驚人的「五連爆」。

6月10日，天津爆炸發生後，當局多採取禁止現場採訪、照相、禁止網間評論。據悉，鄭州市公安支隊爆炸後，警方稱是儲存的化肥因氣溫過高發生自燃引起爆炸。

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Wan Chin: 時局險惡，抗爭維艱，傳授一點政術。

「成大功者，不謀於眾。」並不是說，不與眾人謀，而是不與市井庶民謀。成就大事，靠的是關鍵的少數（critical minority），只要找到關鍵性的同路人，便可以形成滾雪球運動所需要的內核，滾動下去，累積數量。