《数字信号处理》Matlab实验

./《数字信号处理》Matlab实验一．离散信号的FFT分析1.用Matlab编程上机练习。已知：N=2^5。这里Q=0.9+j0.3。可以推导出,首先根据这个式子计算X<k>的理论值,然后计算输入序列x<n>的32个值,再利用基2时间抽选的FFT算法,计算x<n>的DFTX<k>,与X<k>的理论值比较〔要求计算结果最少6位有效数字。解：函数代码：>>functionxn<>>>formatlong>>q=0.9+0.3*i;>>wn=exp<-2*pi*i/32>;>>xk=<1-q^32>./<1-q*wn.^[0:31]>>>xn=q.^[0:31]>>xk1=fft<xn,32>>>diff=xk-xk1具体执行情况：>>functionxn<>formatlongq=0.9+0.3*i;wn=exp<-2*pi*i/32>;xk=<1-q^32>./<1-q*wn.^[0:31]>xk=Columns1through20.5698+3.3840i2.8369+8.8597iColumns3through49.3189-9.8673i1.2052-3.5439iColumns5through61.8846-2.0941i0.8299-1.2413iColumns7through80.9214-1.0753i0.3150-0.0644iColumns9through100.9240-0.8060i0.4202-0.2158iColumns11through120.8513-0.6357i0.5040-0.1701iColumns13through140.6217-0.6931i0.2441-0.8978iColumns15through160.9454-0.2800i0.7139-0.3158iColumns17through180.6723-0.6496i0.0263+0.5093iColumns19through200.5671+0.6914i0.3173+0.9841iColumns21through220.8929+0.7792i0.4066+0.8452iColumns23through240.5847+0.9017i0.9129+0.9283iColumns25through260.0573+0.5531i0.4219+0.9562iColumns27through280.3298+0.3143i0.4513+0.2638iColumns29through300.7214+0.1879i0.0933+1.7793iColumns31through320.9483+1.9802i0.4932+2.6347i>>xn=q.^[0:31]xn=Columns1through21.00000.0000+0.0000iColumns3through40.0000+0.0000i0.0000+0.0000iColumns5through60.0000+0.0000i-0.0000+0.0000iColumns7through8-0.0000+0.0000i-0.0000+0.0000iColumns9through10-0.0000+0.0000i-0.0000+0.0000iColumns11through12-0.0000-0.0000i-0.0000-0.0000iColumns13through14-0.2000-0.4000i-0.3600-0.5200iColumns15through16-0.9680-0.1760i0.4816-0.3488iColumns17through180.2381-0.2695i0.2951-0.1711iColumns19through200.1169-0.4655i0.4449-0.9838iColumns21through220.6955+0.2480i0.5516+0.4319iColumns23through240.3669+0.5542i0.9639+0.2088iColumns25through260.3049+0.9771i-0.5187+0.4709iColumns27through28-0.6081+0.2682i-0.1278+0.5589iColumns29through30-0.4827+0.0647i-0.6538+0.5134iColumns31through32-0.8425-0.4341i-0.1280-0.1434i>>xk1=fft<xn,32>xk1=Columns1through20.5698+3.3839i2.8366+8.8599iColumns3through49.3182-9.8692i1.2051-3.5439iColumns5through61.8845-2.0942i0.8298-1.2413iColumns7through80.9213-1.0754i0.3150-0.0645iColumns9through100.9240-0.8060i0.4202-0.2158iColumns11through120.8514-0.6356i0.5040-0.1701iColumns13through140.6217-0.6931i0.2441-0.8977iColumns15through160.9454-0.2800i0.7139-0.3159iColumns17through180.6723-0.6496i0.0263+0.5093iColumns19through200.5671+0.6913i0.3172+0.9840iColumns21through220.8929+0.7792i0.4065+0.8452iColumns23through240.5846+0.9016i0.9129+0.9283iColumns25through260.0572+0.5531i0.4219+0.9563iColumns27through280.3297+0.3144i0.4512+0.2638iColumns29through300.7213+0.1879i0.0932+1.7793iColumns31through320.9480+1.9802i0.4928+2.6347i>>diff=xk-xk1diff=1.0e-013*Columns1through20.4625+0.8501i0.9504-0.4003iColumns3through40.6010+0.4028i0.4752+0.7001iColumns5through60.5502+0.8501i0.4625+0.8501iColumns7through80.7751+0.9250i0+0.3875iColumns9through100.7751-0.4625i0.3126-0.4625iColumns11through12-0.4625-0.3126i0.4625+0.3875iColumns13through14-0.9250+0.6938i0.3875-0.0781iColumns15through160.3875-0.6156i0+0.9641iColumns17through180.9250-0.7598i-0.4625-0.0422iColumns19through200.4625+0.1172i0.4625+0.3094iColumns21through220.9250+0.4625i0.9250+0.2313iColumns23through240.3875+0.1563i0.3875-0.2313iColumns25through260.8501-0.9250-0.4625iColumns27through280.0127-0.7751i0.7001-0.9250iColumns29through300.16260.7814-0.9250iColumns31through320.4816+0.9250i0.7255-0.8501i由以上结果可知,由基2时间抽选的FFT算法所得到的DFT结果与利用公式法所得的理论值稍有偏差,但误差较小,从结果可以看出大概在小数点第15位才开始出现误差,故而用计算机FFT处理数据在精度上是可以接受的。产生误差的主要原因可能是在计算机进行FFT算法函数的过程中几次蝶形运算所得的中间值会产生舍位上的误差,故而与理论值产生一定的偏差。2.假设信号x<n>由下述信号组成：请选择合适的长度N和窗函数,用DFT分析其频谱,得到清楚的三根谱线。解：函数代码：N=1000;%LengthofDFTn=[0:1:N-1];xn=0.001*cos<0.45*n*pi>+sin<0.3*n*pi>-cos<0.302*n*pi-pi/4>;Xk=fft<xn,N>;k=[0:1:N/2];subplot<2,1,2>;stem<k,abs<Xk<1:1:<N/2+1>>>>;title<'D