《DSP using MATLAB》Problem 5.27

代码：

%% +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%%            Output Info about this m-file
fprintf('\n***********************************************************\n');
fprintf('        <DSP using MATLAB> Problem 5.27 \n\n');

banner();
%% +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++

% -------------------------------------------------------------------
%
% -------------------------------------------------------------------
N = 4;
n1 = [0:3];
x1 = [1, 3, 2, -1];

n2 = [0:3];
x2 = [2, 1, 0, -1];

% -----------------------------------
%     1st way to Linear-Convolution
% -----------------------------------
[y1, ny1] = conv_m(x1, n1, x2, n2);

% --------------------------------------------
%   2nd way ----  circular conv(FREQ domain)
% --------------------------------------------
N2 = length(x1)+length(x2)-1;
y2 = circonvf(x1, x2, N2);
ny2 = ny1;

% ---------------------------------------
%   3rd way --- Cir Conv (TIME domain)
% ---------------------------------------
N3 = length(x1)+length(x2)-1;
y3 = circonvt(x1, x2, N3);
ny3 = ny1;

N4 = 5;
y4 = circonvt(x1, x2, N4);
ny4 = [0:N4-1];

figure('NumberTitle', 'off', 'Name', 'P5.27 x1(n) and x2(n)')
set(gcf,'Color','white');
subplot(2,1,1); stem(n1, x1);
xlabel('n'); ylabel('x1(n)');
title('x1(n), N=4');  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), N=4');  grid on;

figure('NumberTitle', 'off', 'Name', 'P5.27 Convolution')
set(gcf,'Color','white');
subplot(2,2,1); stem(ny1, y1);
xlabel('n'); ylabel('y1(n)');
title('Linear-Conv y1(n), N=7');  grid on;
subplot(2,2,2); stem(ny2, y2);
%axis([-N/2, N/2, -0.5, 50.5]);
xlabel('n'); ylabel('y2(n)');
title('Cir-Conv(FREQ domain) y2(n), N=7');  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(TIME domain) y3(n), N=7');  grid on;
subplot(2,2,4); stem(ny4, y4);
%axis([-N/2, N/2, -0.5, 50.5]);
xlabel('n'); ylabel('y4(n)');
title('Cir-Conv(TIME domain) y4(n), N=5');  grid on;

　　运行结果：

上图中，y1是长度为7的线性卷积结果，y4是5点圆周卷积结果。