代码：

%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++%%            Output Info about this m-filefprintf('\n***********************************************************\n');fprintf('        
     
       Problem 5.33 \n\n');banner();%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++% -------------------------------------------------------------%   x3(n) --- N-point circular convolution of x1(n) an x2(n)  %   x4(n) ---          Linear convolution     %   e(n)  ---       error sequence                            % -------------------------------------------------------------N = 8;n1 = [0:3];x1 = [2, 1, 1, 2];N1 = length(x1);n2 = [0:3];x2 = [1, -1, -1, 1];N2 = length(x2);% --------------------------------------------%        1st way ---- time domain% --------------------------------------------Ny1 = circonvt(x1, x2, N)ny1 = [0:N-1];% --------------------------------------------%   2nd way ----  DFT method% --------------------------------------------y2 = circonvf(x1, x2, N);ny2 = [0:N-1];% --------------------------------------------%   3rd way --- circulant matrix% --------------------------------------------y3 = circonvt_v3(x1, x2, N);ny3 = [0:N-1];% ---------------------------------------%     Linear convolution% ---------------------------------------[y4, ny4] = conv_m(x1, n1, x2, n2);%e1 = y1 - y4(1:N);figure('NumberTitle', 'off', 'Name', 'P5.33 x1(n) and x2(n) N=4')set(gcf,'Color','white'); subplot(2,1,1); stem(n1, x1); xlabel('n'); ylabel('x1(n)');title('x1(n)');  grid on;subplot(2,1,2); stem(n2, x2);  %axis([-N/2, N/2, -0.5, 50.5]);xlabel('n'); ylabel('x2(n)');title('x2(n)');  grid on;figure('NumberTitle', 'off', 'Name', 'P5.33 Cir-Conv(N=8) and Linear-Conv')set(gcf,'Color','white'); subplot(2,2,1); stem(ny1, y1); xlabel('n'); ylabel('y1(n)');title('Cir-Conv (Time domain), y1(n)');  grid on;subplot(2,2,2); stem(ny2, y2);  %axis([0, N, 0, 1]);xlabel('n'); ylabel('y2(n)');title('Cir-Conv (DFT method), y2(n)');  grid on;subplot(2,2,3); stem(ny3, y3);  %axis([-N/2, N/2, -0.5, 50.5]);xlabel('n'); ylabel('y3(n)');title('Cir-Conv (circulant matrix), y3(n)');  grid on;subplot(2,2,4); stem(ny4, y4);  %axis([-N/2, N/2, -0.5, 50.5]);xlabel('n'); ylabel('y4(n)');title('Linear-Conv, y4(n)');  grid on;
     

　　运行结果：

        y1--圆周卷积，N=4；y4---线性卷积，长度为7

        由下图可知，当N=7时，序列的圆周卷积和线性卷积结果相同。

         结论：两序列x1长N1，x2长N2，当N至少取N1+N2-1做圆周卷积，结果和线性卷积相同。