导航：题目详情 | 答案解析 | 相关问题 | 最新问题

已知序列x（n)=4δ（n)＋3δ（n－1)＋2δ（n－2)＋δ（n－3)和它的6点离散傅里叶变换X（k)。

大学 2022-01-24 01:34:24 序列已帮助人

已知序列x(n)=4δ(n)+3δ(n-1)+2δ(n-2)+δ(n-3)和它的6点离散傅里叶变换X(k)。

热搜：n维列向量组a1,an-1线性无关,且与非零向量正交

答案解析

难度★★☆ 搜索

由 $latex.action?latex=WShrKT1XX3s2fV57NGt9WChrKQ%3D%3D$ 知，y(n)是x(n)向右循环移位4的结果，即
y(n)=x((n-4))6
=4δ(n-4)+3δ(n-5)+2δ(n)+δ(n-1)$ $latex.action?latex=WChrKT1cc3VtIF97bj0wfV57NX1bNFxkZWx0YSAobikrM1xkZWx0YSAobi0xKSsyXGRlbHRhIChu%0D%0ALTIpK1xkZWx0YSAobi0zKV1XX3s2fV57bmt9$
$latex.action?latex=PTQrM1dfezZ9XntrfSsyV197Nn1eezJrfStXX3s2fV57M2t9$
$latex.action?latex=WF4qKGspPTQrM1dfezZ9Xnsta30rMldfezZ9XnstMmt9K1dfezZ9XnstM2t9$
$latex.action?latex=UmVbWChrKV09XGZyYWN7MX17Mn1bWChrKStYXiooayld$
$latex.action?latex=PVxmcmFjezF9ezJ9WzQrM1dfezZ9XntrfSsyV197Nn1eezJrfStXX3s2fV57M2t9KzQrM1dfezZ9%0D%0AXnsta30rMldfezZ9XnstMmt9K1dfezZ9XnstM2t9XQ%3D%3D$
$latex.action?latex=PVxmcmFjezF9ezJ9WzgrM1dfezZ9XntrfSsyV197Nn1eezJrfStXX3s2fV57M2t9KzNXX3s2fV57%0D%0ANWt9KzJXX3s2fV57NGt9K1dfezZ9Xnsza31d$
$latex.action?latex=PVxmcmFjezF9ezJ9WzgrM1dfezZ9XntrfSsyV197Nn1eezJrfSsyV197Nn1eezNrfSsyV197Nn1e%0D%0AezRrfSszV197Nn1eezVrfV0%3D$
由上式得到
$latex.action?latex=dShuKT00XGRlbHRhIChuKStcZnJhY3szfXsyfVxkZWx0YSAobi0xKStcZGVsdGEgKG4tMik%3D$
$latex.action?latex=dShuKT00XGRlbHRhIChuKStcZnJhY3szfXsyfVxkZWx0YSAobi0xKStcZGVsdGEgKG4tMikrXGRl%0D%0AbHRhIChuLTMpK1xkZWx0YSAobi00KStcZnJhY3szfXsyfVxkZWx0YSAobi01KQ%3D%3D$ $ $latex.action?latex=WCgyayk9XHN1bSBfe249MH1eezV9eChuKVdfezZ9Xnsybmt9PVxzdW0gX3tuPTB9Xns1fXgobilX%0D%0AX3szfV57bmt9$
$latex.action?latex=PVxzdW0gX3tuPTB9XnsyfXgobilXX3szfV57bmt9K1xzdW0gX3tuPTN9Xns1fXgobilXX3szfV57%0D%0Abmt9$
$latex.action?latex=PVxzdW0gX3tuPTB9XnsyfXgobilXX3szfV57bmt9K1xzdW0gX3tuPTB9XnsyfXgobiszKVdfezN9%0D%0AXntrKG4rMyl9$
$latex.action?latex=PVxzdW0gX3tuPTB9XnsyfXgobilXX3szfV57bmt9K1dfezN9Xnsza31cc3VtIF97bj0wfV57Mn14%0D%0AKG4rMylXX3szfV57bmt9$
$latex.action?latex=PVxzdW0gX3tuPTB9XnsyfVt4KG4pK3gobiszKV1XX3szfV57bmt977yMaz0w77yMMe%2B8jDI%3D$
由于 $latex.action?latex=VihrKT1cc3VtIF97bj0wfV57Mn12KG4pV197M31ee25rfT1YKDJrKQ%3D%3D$
$latex.action?latex=PVxzdW0gX3tuPTB9XnsyfVt4KG4pK3gobiszKV1XX3szfV57bmt977yMaz0w77yMMe%2B8jDI%3D$
所以 v(n)=x(n)+x(n+3)， n=0，1，2
即 v(0)=x(0)+x(3)=5
v(1)=x(1)+x(4)=3
v(2)=x(2)+x(5)=2
或 v(n)=5δ(n)+3δ(n-1)+2δ(n-2)