山东大学2014-2015学年2学期数字信号处理（双语）课程试卷(4) 得分港人 5.(10 pts)The figure below shows the flow graph for an 8-point decimation-in-time FFT algorithm.The heavy line shows a path from sample x7]to DFT sample X[21. X 都 o XT到 [3]o X[ 洲 7- (a)What is the"gain"along the path that is emphasized in the Figure above? (b)How many other paths in the flow graph begin at and end at X[2?Is this true in general?That is, how many paths are there between each input sample and each output sample? (c)Now consider the DFT sample X[2].By tracing paths in the flow graph of the Figure above,show that each input sample contributes the proper amount to the output DFT sample X2];i.e find the bin] (n=0,1,..,7)in the cquation: Xp]-之物 器 第4项共5页2014-2015 2 数字信号处理（双语） （A） 4 5 5．(10 pts) The figure below shows the flow graph for an 8-point decimation-in-time FFT algorithm. The heavy line shows a path from sample x[7] to DFT sample X[2]. (a) What is the "gain" along the path that is emphasized in the Figure above? (b) How many other paths in the flow graph begin at x[7] and end at X[2]? Is this true in general? That is, how many paths are there between each input sample and each output sample? (c) Now consider the DFT sample X[2]. By tracing paths in the flow graph of the Figure above, show that each input sample contributes the proper amount to the output DFT sample X[2]; i.e., find the b[n] (n=0, 1, .. ,7) in the equation:   7 0 2 [ ] [ ] n X x n b n = =  得分 阅卷人