数字信号处理ii习题解答(老师版)

1、A sinusoidal signal is applied to a second-order linear predictor as in Fig.1 . Calculate the theoretical ACF(Auto-Correlation Function) of the signal and the prediction coefficients. Verify that the zeros of the FIR prediction filter are on the unit circle at the right frequency.Using the LMS algor

2、ithm with , show the evolution of the coefficients from time to . How is that evolution modified if the sign algorithm is used instead. Fig.1. Second-order prediction filter解：计算预测系数理论值(滤波器系数的维纳最优解)，由，输出最小均方误差理论值可由下式计算:其中FIR滤波器零点：,即零点在正弦信号x(n)频率的对应的z平面位置.用LMS算法，n010时系数的近似值LMS：在线性预测误差滤波的LMS算法中：所以, LMS

3、算法下的预测误差滤波器符号算法A second-order adaptive FIR filter has the input as andas reference signal. Calculate the coefficients, starting from zero initial values, from time n=0 to n = 10 . Calculate the theoretical residual error and the time constant and compare with the experimental results.(解：取计算n010的系数，

4、Theoretical residual error: Theoretical time constant：注意: 由于均方收敛的时间常数比均值收敛的时间常数小, 所以实际应用中采用较保守的理论估计值,即采用均值收敛的时间常数作为算法收敛的时间常数的理论估计值.利用（2）（3）作迭代：，根据实验结果计算残差和时间常数残差 = 时间常数:通过观察见,在n为偶数时, 误差变化波动大, 因此应选择在n为奇数时的误差值确定时间常数较合理.所以实验结果和理论值是符合的.Adaptive line enhancer. Consider an adaptive third-order FIR predict

5、or. The input signal is where is a white noise with power .Calculate the optimal coefficients . Give the noise power in the sequence as well as the signal power. Calculate the SNR enhancement.解：计算，由于窄带信号为白噪声，时延参数D选择1。原而 （信号） （噪声）所以此时Use the Levinson-Dubin algorithm to compute the PARCOR coefficients

6、 (反射系数) associated with the correlation sequenceGive the diagram of the lattice filter with three sections. Comment on the case 解：计算LD反射系数初始化， ，lattice预测器结构，由以上结果可知, 当时, 预测器变为一阶预测器,说明此时输入信号是AR(1)信号。即The definition of the discrete STFT of a digital signal is as following:，(-window function,-length of

7、 )。Please explain the above discrete STFT from filtering point and demonstrate the OLA method of the inverse discrete STFT(即证明离散STFT反变换的OLA法,有时又称着OLA综合方法)。解：从低通和带通两种角度解释。证明请查阅课堂笔记。A signal is the output of a linear system as in Fig.2 excited by a unit impulse signal . Fig.2 Second-order IIR Filterverify that the signal is a minimum phase signal.(最小相位信号)解：由Fig.2，输出的Z-变换为，所以信号的极点为=-0.4，=0.5，零点为=0，即信号的Z-变换的所有零、极点均在单位圆内，故是最小相位信号.(a) 简述最大熵谱估计与参数模型法谱估计的原理；从传统谱估计法存在的缺点及其原因出发讨论最大熵谱估计与参数模型法谱估计的优点。(b) 讨