Hello. I have 2 very serious questions that I am confused. It is quite hurry.
1.) Suppose I got a plot, and I want to find its function. This plot below is taken from my book,
圖片參考：http://imgcld.yimg.com/8/n/HA00799676/o/701112170012113873412240.jpg
and this one by observed is a sin function, x[n] = c * sin( 2*pi*n / 6 )
c is just a constant, and the period is 2* pi / 6.
My question is, how do I know it is a sin function but not a cos function?
2.) Another plot taken from my book, and x[n]= (1/2) + (1/2)*(-1)^n
圖片參考：http://imgcld.yimg.com/8/n/HA00799676/o/701112170012113873412251.jpg
Are there any tips or ways for me to figure out what the function is ( x[n] = ? ) when I see plots ? Like if I see other plots, how do I figure out the x[n]. Give me an example please.
Thanks a lot. Your explanation will save my life.
Recognize function from plot
2011-12-17 3:37 pm
回答 (3)
2011-12-17 5:49 pm
✔ 最佳答案
1.sin curve starts from zero position when n = 0
cos curve starts from max position when n = 0
but they are actually same with a shift only, e.g. sin x = cos (pi/2 - x)
cos (pi/2 - x) = cos(pi/2)cos(-x) - sin(pi/2)sin(-x)
cos (pi/2 - x) = 0 - sin(-x) = sin x
2.
it can interpreted as a cos curve with a upward shift 0.5
amplitude is 0.5 with period = 2pi / 4
x[n] = upward shift + Amplitude cos [2n(pi)/4 + horizontal shift]
x[n] = 0.5 + 0.5 cos [2n(pi)/4 + C]
x[n] = 0.5 + 0.5 cos [n(pi)/2 + C]
when n = 0 => x[n] = 1 => C = 0
x[n] = 0.5 + 0.5 cos [n(pi)/2]
...
2011-12-21 4:32 pm
圖片參考：http://i212.photobucket.com/albums/cc82/doraemonpaul/yahooknowledge/periodicfunction9.jpg
參考資料：
my wisdom of maths
2011-12-17 7:43 pm
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