已知序列
x
(
n
)
x(n)
x(n),长度为N,要通过插零方式扩展至原来的r倍,
通过数字信号插零公式:
y ( n ) = { x ( n r ) , n = i r , i = 0 ∼ N − 1 , 0 , e l s e . \bm{y(n)=\left\{ \begin{array}{l} x(\frac{n}{r}),n=ir,i=0 \sim N-1,\\ 0,\quad \quad \quad else. \end{array} \right.} y(n)={x(rn),n=ir,i=0∼N−1,0,else.
举例说明:
则当 n 取 0 , 2 , 4 , 6 时 , x ( n r ) n取0,2,4,6时,x(\frac{n}{r}) n取0,2,4,6时,x(rn)分别等于原 x ( n ) x(n) x(n)的 x ( 0 ) x(0) x(0), x ( 1 ) x(1) x(1) , x ( 2 ) ,x(2) ,x(2), x ( 3 ) x(3) x(3)的值,其余为0,
即 x ( n r ) = { 1 , 0 , 2 , 0 , 3 , 0 , 4 , 0 } x(\frac{n}{r})=\{1,0,2,0,3,0,4,0\} x(rn)={1,0,2,0,3,0,4,0},即通过间插方式扩展为原来的2倍。
则当 n 取 0 , 3 , 6 , 9 时 , x ( n r ) n取0,3,6,9时,x(\frac{n}{r}) n取0,3,6,9时,x(rn)分别等于原 x ( n ) x(n) x(n)的 x ( 0 ) x(0) x(0), x ( 1 ) x(1) x(1) , x ( 2 ) ,x(2) ,x(2), x ( 3 ) x(3) x(3)的值,其余为0,
即 x ( n r ) = { 1 , 0 , 0 , 2 , 0 , 0 , 3 , 0 , 0 , 4 , 0 , 0 } x(\frac{n}{r})=\{1,0,0,2,0,0,3,0,0,4,0,0\} x(rn)={1,0,0,2,0,0,3,0,0,4,0,0},即通过间插方式扩展为原来的3倍。