数字图像处理DSP实验二第三章Word文档下载推荐.docx
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N='
nn=0:
(1/N):
1;
mm=(1-(1/N)):
(-1/N):
num=[nn,mm];
den=[zeros(1,N),1];
%Computethefrequencyresponse
w=0:
pi/(k-1):
pi;
h=freqz(num,den,w);
%Plotthefrequencyresponse
subplot(2,2,1)
plot(w/pi,real(h));
grid
title('
Realpart'
)
xlabel('
\omega/\pi'
ylabel('
Amplitude'
subplot(2,2,2)
plot(w/pi,imag(h));
Imaginarypart'
subplot(2,2,3)
plot(w/pi,abs(h));
MagnitudeSpectrum'
Magnitude'
subplot(2,2,4)
plot(w/pi,angle(h));
PhaseSpectrum'
Phase,radians'
同理,使用zerophase函数得出准确的频率响应如下
Numberoffrequencypoints='
%Readinthenumeratoranddenominatorcoefficients
0;
den=[zeros(1,N),1,zeros(1,N)];
h=zerophase(num,den,w);
%求频率响应
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
%
%Readinthedesirednumberoffrequencysamples
num=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]'
使用zerophase函数的代码如下:
Numeratorcoefficients=(a)[1zeros(1,41)-1]...(d)[-0.25000-11zeros(1,4)0.5zeros(1,4)1-1000-0.25]'
Denominatorcoefficients=(a)[zeros(1,20)10-1zeros(1,23)]...(d)[zeros(1,9)-12-1zeros(1,9)]'
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:
nn=-N:
1:
N;
num=cos(pi/20.*nn);
M3.3画出如下DTFT的实部和虚部以及幅度和相位谱
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=[1,0.1386,0.8258,0.1393,0.4153]进行运算
num=0.1323.*[1,0.1444,-0.4519,0.1444,1];
den=[1,0.1386,0.8258,0.1393,0.4153];
同理,直接可提取分子的系数num=0.3192.*[1,0.1885,-0.1885,-1],分母的系数den=[1,0.7856,1.4654,-0.2346],利用freqz函数进行运算
num=0.3192.*[1,0.1885,-0.1885,-1];
den=[1,0.7856,1.4654,-0.2346];
M3.5验证表3.2列出的复序列的DTFT的对称关系
1.反转
【codes】
%property1
N=8;
a=0.5;
n=0:
N-1;
x=exp(j*a*n);
[Xw]=freqz(x,1,512);
y=exp(j*a*fliplr(n));
m=0:
511;
w=-pi*m/512;
[Y1w]=freqz(y,1,w);
Y=exp(j*w*(N-1)).*Y1;
plot(w/pi,abs(X));
x[n]MagnitudeSpectrum'
plot(w/pi,angle(X));
x[n]PhaseSpectrum'
plot(w/pi,abs(Y));
y[n]MagnitudeSpectrum'
plot(w/pi,angle(Y));
y[n]PhaseSpectrum'
2.共轭反转对称
%property2
y=exp(-j*a*fliplr(n));
[Y1w]=freqz(y,1,512);
Y=conj(exp(j*w*(N-1)).*Y1);
【图形】
性质三
%property3
y=real(x);
[X0w]=freqz(x,1,512);
%X0为x的DTFT
[Yw]=freqz(y,1,512);
%Y为y的DTFT
w0=-pi*m/512;
[X1w]=freqz(x,1,w0);
%X1为x(exp(-j*w))的DTFT
M=conj(X1);
X=0.5*(X0+M'
性质四
y=j*imag(x);
X=0.5*(X0-M'
结论:
由图可以看出,性质三、四得到的傅里叶变换也满足对称关系,由于计算存在精度误差,此处未比较相位谱,采用比较的是实部和虚部,尽管图形不一定完全吻合,但也能基本看出其的大小关系。
性质五、六
xcs=0.5*[zeros(1,N-1)x]+0.5*[yzeros(1,N-1)];
xca=0.5*[zeros(1,N-1)x]-0.5*[yzeros(1,N-1)];
[Y1w]=freqz(xcs,1,512);
[Y2w]=freqz(xca,1,512);
%X为x的DTFT
Y1=Y1.*exp(j*w*(N-1));
%Y1为xcs的DTFT
Y2=Y2.*exp(j*w*(N-1));
%Y2为xca的DTFT
subplot(3,2,1)
plot(w/pi,real(X));
XRealpart'
subplot(3,2,2)
plot(w/pi,imag(X));
XImaginarypart'
subplot(3,2,3)
plot(w/pi,real(Y1));
Y1Realpart'
subplot(3,2,4)
plot(w/pi,imag(Y1));
Y1Imaginarypart'
subplot(3,2,5)
plot(w/pi,real(Y2));
Y2Realpart'
subplot(3,2,