山东大学2015-2016学年2学期数字信号处理（双语）课程试卷()答案与评分细则 5.(15 pts)Proof:Since[]] =2x时=差xw (3 pts) (4 pts) : x时 -星片2xs (4pts) -2s[a-儿]0sasw-l (4 pts) 6.(10 pts)Solution: The array DIr]can be expressed in terms of C[r]: D[o=C[0+c4:D[0=C[刊+C[:D[2=C[2]+wC[D[3)=C[3+wc[ D[4=Co-C4:D[=C-C[:D[=C2-c[:D[]=C[-wC[]: (4 pts) Solving the equations above for CIr]gives c[0=c[0=c2]=c[3-1:c[4-C-c=c]=o. (4 pts) For r,1...,a sketch of the sequence C[r]is provided below. 器 i 12 (2pts) 第2页共2页2015-2016 2 数字信号处理（双语） （A）答案与评分细则 2 2 5．(15 pts) Proof: Since X k X k X k 3 1 2   =         1 3 3 0 1 N kn N k x n X k W N − − = =      1 1 2 0 1 N kn N k X k X k W N − − = =  (3 pts)     1 1 1 2 0 0 1 N N km kn N N k m x m W X k W N − − − = =   =       (4 pts)     ( ) 1 1 1 2 0 0 1 N N k n m N m k x m X k W N − − − − = = =   (4 pts)   (( )) 1 1 2 0 , 0 1 N N m x m x n m n N − = = −   −      (4 pts) 6．(10 pts) Solution: The array D[r] can be expressed in terms of C[r]: D C C 0 0 4  = +     ;       1 8 D C W C 1 1 5 = + ;       2 8 D C W C 2 2 6 = + ;       3 8 D C W C 3 3 7 = + ; D C C 4 0 4  = −     ;       1 8 D C W C 5 1 5 = − ;       2 8 D C W C 6 2 6 = − ;       3 8 D C W C 7 3 7 = − ; (4 pts) Solving the equations above for C[r] gives C C C C 0 1 2 3 1  = = = =       ; C C C C 4 5 6 7 0  = = = =       . (4 pts) For r=0, 1, ... ,7, a sketch of the sequence C[r] is provided below. (2 pts)