已知序列x(n)={1,0,1,1,1},试计算(1)x(n)*x(n) (2)x(n)⑤x(n) (3)x(n)⑩x(n)
时间: 2023-09-25 08:10:56 浏览: 115
计算x的n次方
1. x(n)*x(n)表示两个序列的卷积,计算如下:
x(n)*x(n) = {1,0,1,1,1} * {1,0,1,1,1}
= 1*1 + 0*1 + 1*0 + 1*1 + 1*1 + 0*1 + 0*0 + 0*1 + 0*1 + 0*1
= {1,1,2,3,2,1}
2. x(n)⁵表示将序列x(n)连乘5次,计算如下:
x(n)⁵ = x(n) * x(n) * x(n) * x(n) * x(n)
= {1,0,1,1,1} * {1,0,1,1,1} * {1,0,1,1,1} * {1,0,1,1,1} * {1,0,1,1,1}
= {1,0,1,1,1,0,1,1,0,0,0,0,0,0,0,0,1,1,0,1}
3. x(n)¹⁰表示将序列x(n)连乘10次,计算如下:
x(n)¹⁰ = x(n) * x(n) * x(n) * x(n) * x(n) * x(n) * x(n) * x(n) * x(n) * x(n)
= {1,0,1,1,1} * {1,0,1,1,1} * {1,0,1,1,1} * {1,0,1,1,1} * {1,0,1,1,1} * {1,0,1,1,1} * {1,0,1,1,1} * {1,0,1,1,1} * {1,0,1,1,1} * {1,0,1,1,1}
= {1,0,1,1,1,0,1,1,0,0,1,1,0,1,1,0,1,1,0,1}
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