Question

MATLAB中的fft后为何要用fftshift？

Answer 1

即对频域的图像，（假设用一条水平线和一条垂直线将频谱图分成四块）对这四块进行对角线的交换与反对角线的交换FFTSHIFT Shift zero-frequency component to center of spectrum. For vectors, FFTSHIFT(X) swaps（交换） the left and right halves of X. For matrices, FFTSHIFT(X) swaps the first and third quadrants and the second and fourth quadrants. For N-D arrays, FFTSHIFT(X) swaps "half-spaces" of X along eachdimension. FFTSHIFT(X,DIM) applies the FFTSHIFT operation along the dimension DIM. FFTSHIFT is useful for visualizing the Fourier transform with the zero-frequency component in the middle of the spectrum.fftshift就是对换数据的左右两边比如 x=[1 2 3 4] fftshift(x) ->[3 4 1 2] IFFTSHIFT Inverse FFT shift.（就是fftshift的逆）x=[1 2 3 4 5];y=fftshift(x)y = 4 5 1 2 3ifftshift(y)ans = 1 2 3 4 5 IFFTSHIFT undoes the effects of FFTSHIFT. 注意：在使用matlab的fft及fftshift时，应注意。假定采样频率fs，采样间隔dt，采样点数N。fftshift后的频率为-2，-1，0，1，2对于二维fftshift，其与直接用下面的结果一样if mod(tempN,2)==0 kx=(0:tempM-1)/tempM/dx-tempM/2/tempM/dx;% kx=kx*2*pielse kx=(0:tempM-1)/tempM/dx-(tempM-1)/2/tempM/dx;% kx=kx*2*piendkx=kx*2*pi;if mod(tempM,2)==0 ky=(0:tempN-1)/tempN/dy-tempN/2/tempN/dy;% kx=kx*2*pielse ky=(0:tempN-1)/tempN/dy-(tempN-1)/2/tempN/dy;% kx=kx*2*piendky=ky*2*pi;temp1=sqrt(kx.^2+ky.^2);k1=temp1;[kx,ky]=meshgrid(kx,ky);如下面程序表明上面两个相同：dx=50e3; dy=50e3;% % % % % % % % % % % tempN=41;tempM=41;% % % % % % % % % % % % % % % %determining the wavenumber kx and kyif mod(tempM,2)==0 kx=(0:tempM-1)-tempM/2;% kx=kx*2*pielse kx=(0:tempM-1)-(tempM-1)/2;% kx=kx*2*piendkx=kx*2*pi/tempM/dx;if mod(tempN,2)==0 ky=(0:tempN-1)-tempN/2;% kx=kx*2*pielse ky=(0:tempN-1)-(tempN-1)/2;% kx=kx*2*piendky=ky*2*pi/tempN/dy;[kxx,kyy]=meshgrid(kx,ky);k00=sqrt(kx.^2+ky.^2);% % % % % % % % % % % % % % % % if mod(tempM,2)==0 temp1=tempM/2-1; temp2=(temp1+1):(tempM-1); temp2=temp2-tempM; temp3=[0:temp1,temp2]; kx=temp3/tempM/dx;% kx=kx*2*pielse temp1=(tempM-1)/2; temp2=(temp1+1):(tempM-1); temp2=temp2-tempM; temp3=[0:temp1,temp2]; kx=temp3/tempM/dx;% kx=kx*2*piendkx=kx*2*pi;if mod(tempN,2)==0 temp1=tempN/2-1; temp2=(temp1+1):(tempN-1); temp2=temp2-tempN; temp3=[0:temp1,temp2]; ky=temp3/tempN/dy;% kx=kx*2*pielse temp1=(tempN-1)/2; temp2=(temp1+1):(tempN-1); temp2=temp2-tempN; temp3=[0:temp1,temp2]; ky=temp3/tempN/dy;% kx=kx*2*piendky=ky*2*pi;[kx,ky]=meshgrid(kx,ky);kx=fftshift(kx);ky=fftshift(ky);k=sqrt(kx.^2+ky.^2);figuresubplot(3,1,1),contourf(kxx-kx)subplot(3,1,2),contourf(kyy-ky)subplot(3,1,3),contourf(k00-k)%%%%%%%%%%%fft及fftshift示例： clf;fs=100;N=256; %采样频率和数据点数n=0:N-1;t=n/fs; %时间序列x=0.5*sin(2*pi*15*t)+2*sin(2*pi*40*t); %信号y1=fft(x,N); %对信号进行快速Fourier变换y2=fftshift(y1);mag1=abs(y1); %求得Fourier变换后的振幅mag2=abs(y2); f1=n*fs/N; %频率序列f2=n*fs/N-fs/2;%这个未必正确subplot(3,1,1),plot(f1,mag1,'r'); %绘出随频率变化的振幅xlabel('频率/Hz');ylabel('振幅');title('图1：usual FFT','color','r');grid on;subplot(3,1,2),plot(f2,mag1,'b'); %绘出随频率变化的振幅xlabel('频率/Hz');ylabel('振幅');title('图2：FFT without fftshift','color','b');grid on;subplot(3,1,3),plot(f2,mag2,'c'); %绘出随频率变化的振幅xlabel('频率/Hz');ylabel('振幅');title('图3：FFT after fftshift','color','c');grid on;