数字图像处理DSP实验二第三章

第三章M3.2求解并画出当N=10时，习题3.18中的序列的DTFT的实部和虚部以及幅度和相位谱解析：根据3.18题中计算得到的DTFT，分子分母化为exp(-j*w*n)的多项式之和，将分子分母每一项的系数分别组成矩阵num,dem,再利用freqz函数进行运算，可得的如下结果【图形】00.51-100102030Realpart/Amplitude00.51-5051015x10-14Imaginarypart/Amplitude00.510102030MagnitudeSpectrum/Magnitude00.51-4-2024PhaseSpectrum/Phase,radians可以看出该频率响应的虚部实际为0，即其应为零相位谱，故使用zerophase函数更加准确的画出的其频率响应如下所示：00.10.20.30.40.50.60.70.80.91-50510152025/Amplitude【图形】00.51-5051015Realpart/Amplitude00.51-1001020Imaginarypart/Amplitude00.510102030MagnitudeSpectrum/Magnitude00.51-4-2024PhaseSpectrum/Phase,radians解析：本题采用定义式求其傅里叶变换，再变换为相应形式求得需要的系数向量，相应代码如下：【代码】%ReadinthedesirednumberoffrequencysamplesNk=input('Numberoffrequencypoints=');%ReadinthelengthNN=input('N=');nn=0:(1/N):1;mm=(1-(1/N)):(-1/N):0num=[nn,mm];den=[zeros(1,N),1];%Computethefrequencyresponsew=0:pi/(k-1):pi;h=freqz(num,den,w);%Plotthefrequencyresponsesubplot(2,2,1)plot(w/pi,real(h));gridtitle('Realpart')xlabel('\omega/\pi');ylabel('Amplitude')subplot(2,2,2)plot(w/pi,imag(h));gridtitle('Imaginarypart')xlabel('\omega/\pi');ylabel('Amplitude')subplot(2,2,3)plot(w/pi,abs(h));gridtitle('MagnitudeSpectrum')xlabel('\omega/\pi');ylabel('Magnitude')subplot(2,2,4)plot(w/pi,angle(h));gridtitle('PhaseSpectrum')xlabel('\omega/\pi');ylabel('Phase,radians')【图形】00.510510Realpart/Amplitude00.51-4-202x10-15Imaginarypart/Amplitude00.510510MagnitudeSpectrum/Magnitude00.51-10123x10-13PhaseSpectrum/Phase,radians同理，使用zerophase函数得出准确的频率响应如下【代码】k=input('Numberoffrequencypoints=');%ReadinthenumeratoranddenominatorcoefficientsN=input('N=');nn=0:(1/N):1;mm=(1-(1/N)):(-1/N):0;num=[nn,mm];den=[zeros(1,N),1,zeros(1,N)];%Computethefrequencyresponsew=0:pi/(k-1):pi;h=zerophase(num,den,w);%求频率响应%Plotthefrequencyresponseplot(w/pi,real(h));gridxlabel('\omega/\pi');ylabel('Amplitude')【图形】00.10.20.30.40.50.60.70.80.91012345678910/Amplitude【图形】00.51-2002040Realpart/Amplitude00.51-10123x10-13Imaginarypart/Amplitude00.51010203040MagnitudeSpectrum/Magnitude00.51-4-2024PhaseSpectrum/Phase,radians同理，使用zerophase函数得出准确的频率响应如下00.10.20.30.40.50.60.70.80.91-50510152025303540/Amplitude以上（a)~(d)四道题的代码如下，（输入时按照括号里相应的题号提示进行矩阵输入）使用freqz函数的代码如下%Program3_2%Discrete-TimeFourierTransformComputation%%Readinthedesirednumberoffrequencysamplesk=input('Numberoffrequencypoints=');%Readinthenumeratoranddenominatorcoefficientsnum=input('Numeratorcoefficients=(a)[1zeros(1,41)-1](b)[1-1zeros(1,8)-1](c)[-0.5zeros(1,9)1zeros(1,9)-0.5](d)[-0.25000-11zeros(1,4)0.5zeros(1,4)1-1000-0.25]');den=input('Denominatorcoefficients=(a)[zeros(1,20)10-1]...(b)[1,-1]...(c)[zeros(1,8)-5,10,-5](d)[zeros(1,9)-12-1]');%Computethefrequencyresponsew=0:pi/(k-1):pi;h=freqz(num,den,w);%求频率响应%Plotthefrequencyresponsesubplot(2,2,1)plot(w/pi,real(h));gridtitle('Realpart')xlabel('\omega/\pi');ylabel('Amplitude')subplot(2,2,2)plot(w/pi,imag(h));gridtitle('Imaginarypart')xlabel('\omega/\pi');ylabel('Amplitude')subplot(2,2,3)plot(w/pi,abs(h));gridtitle('MagnitudeSpectrum')xlabel('\omega/\pi');ylabel('Magnitude')subplot(2,2,4)plot(w/pi,angle(h));gridtitle('PhaseSpectrum')xlabel('\omega/\pi');ylabel('Phase,radians')使用zerophase函数的代码如下：k=input('Numberoffrequencypoints=');%Readinthenumeratoranddenominatorcoefficientsnum=input('Numeratorcoefficients=(a)[1zeros(1,41)-1]...(d)[-0.25000-11zeros(1,4)0.5zeros(1,4)1-1000-0.25]');den=input('Denominatorcoefficients=(a)[zeros(1,20)10-1zeros(1,23)]...(d)[zeros(1,9)-12-1zeros(1,9)]');%Computethefrequencyresponsew=0:pi/(k-1):pi;h=zerophase(num,den,w);%求频率响应%Plotthefrequencyresponseplot(w/pi,real(h));gridxlabel('\omega/\pi');ylabel('Amplitude')解析：本题发现其傅里叶变换并不好求，于是换种思路，采用定义式求其傅里叶变换，再变换为相应形式求得需要的系数向量，相应代码如下：【代码】%ReadinthedesirednumberoffrequencysamplesNk=input('Numberoffrequencypoints=');%ReadinthelengthNN=input('N=');nn=-N:1:N;num=cos(pi/20.*nn);den=[zeros(1,N),1];%Computethefrequencyresponsew=0:pi/(k-1):pi;h=freqz(num,den,w);%Plotthefrequencyresponsesubplot(2,2,1)plot(w/pi,real(h));gridtitle('Realpart')xlabel('\omega/\pi');ylabel('Amplitude')subplot(2,2,2)plot(w/pi,imag(h));gridtitle('Imaginarypart')xlabel('\omega/\pi');ylabel('Amplitude')subplot(2,2,3)plot(w/pi,abs(h));gridtitle('MagnitudeSpectrum')xlabel('\omega/\pi');ylabel('Magnitude')subplot(2,2,4)plot(w/pi,angle(h));gridtitle('PhaseSpectrum')xlabel('\omega/\pi');ylabel('Phase,radians')【图形】00.51-5051015Realpart/Amplitude00.51-505x10-15Imaginarypart/Amplitude00.51051015MagnitudeSpectrum/Magnitude00.51-4-2024PhaseSpectrum/Phase,radians同理，使用zerophase函数得出准确的频率响应如下【代码】k=input('Numberoffrequencypoints=');%ReadinthenumeratoranddenominatorcoefficientsN=input('N=');nn=-N:1:N;num=cos(pi/20.*nn);den=[zeros(1,N),1,zeros(1,N)];%Computethefrequencyresponsew=0:pi/(k-1):pi;h=zerophase(num,den,w);%求频率响应%Plotthefrequencyresponseplot(w/pi,real(h));gridxlabel('\omega/\pi');ylabel('Amplitude')【图形】00.10.20.30.40.50.60.70.80.91-202468101214/AmplitudeM3.3画出如下DTFT的实部和虚部以及幅度和相位谱解析：下面两题的表示形式已经满足了freqz函数对分子分母表达形式的要求，直接可提取分子的系数num=0.1323.*[1,0.1444,-0.4519,0.1444,1]，分母的系数den=[1,0.1386,0.8258,0.1393,0.