數(shù)字信號處理ii習(xí)題解答(老師版)

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：計算預(yù)測系數(shù)理論值(濾波器系數(shù)的維納最優(yōu)解)，由，輸出最小均方誤差理論值可由下式計算:其中FIR濾波器零點：,即零點在正弦信號x(n)頻率的對應(yīng)的z平面位置.用LMS算法，n010時系數(shù)的近似值LMS：在線性預(yù)測誤差濾波的LMS算法中：所以, LMS

3、算法下的預(yù)測誤差濾波器符號算法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：取計算n010的系數(shù)，

4、Theoretical residual error: Theoretical time constant：注意: 由于均方收斂的時間常數(shù)比均值收斂的時間常數(shù)小, 所以實際應(yīng)用中采用較保守的理論估計值,即采用均值收斂的時間常數(shù)作為算法收斂的時間常數(shù)的理論估計值.利用（2）（3）作迭代：，根據(jù)實驗結(jié)果計算殘差和時間常數(shù)殘差 = 時間常數(shù):通過觀察見,在n為偶數(shù)時, 誤差變化波動大, 因此應(yīng)選擇在n為奇數(shù)時的誤差值確定時間常數(shù)較合理.所以實驗結(jié)果和理論值是符合的.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：計算，由于窄帶信號為白噪聲，時延參數(shù)D選擇1。原而 （信號） （噪聲）所以此時Use the Levinson-Dubin algorithm to compute the PARCOR coefficients

6、 (反射系數(shù)) associated with the correlation sequenceGive the diagram of the lattice filter with three sections. Comment on the case 解：計算LD反射系數(shù)初始化， ，lattice預(yù)測器結(jié)構(gòu)，由以上結(jié)果可知, 當時, 預(yù)測器變?yōu)橐浑A預(yù)測器,說明此時輸入信號是AR(1)信號。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(即證明離散STFT反變換的OLA法,有時又稱著OLA綜合方法)。解：從低通和帶通兩種角度解釋。證明請查閱課堂筆記。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.(最小相位信號)解：由Fig.2，輸出的Z-變換為，所以信號的極點為=-0.4，=0.5，零點為=0，即信號的Z-變換的所有零、極點均在單位圓內(nèi)，故是最小相位信號.(a) 簡述最大熵譜估計與參數(shù)模型法譜估計的原理；從傳統(tǒng)譜估計法存在的缺點及其原因出發(fā)討論最大熵譜估計與參數(shù)模型法譜估計的優(yōu)點。(b) 討