《DSP using MATLAB》Problem 5.3

这段时间爬山去了，山中林密荆棘多，沟谷纵横，体力增强不少。

代码：

%% ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
%%            Output Info about this m-file
fprintf('\n***********************************************************\n');
fprintf('        <DSP using MATLAB> Problem 5.3 \n\n');

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

% ------------------------------------------
%  1  x1(n)=5sin(0.1pi*n)   n=[0:19], N=40
% ------------------------------------------
L = 20; n = [0:L-1]; N = 40; k = [-N/2:N/2];             % wave parameters
xn_1 = [5*sin(0.1*pi*n), zeros(1, N-L)];
Xk_1 = dfs(xn_1, N);                                     % DFS
magXk = abs( [Xk_1(N/2+1 : N) Xk_1(1 : N/2+1)] );        % DFS magnitude
angXk = angle( [Xk_1(N/2+1 : N) Xk_1(1 : N/2+1)] )/pi;   % DFS angle

figure('NumberTitle', 'off', 'Name', 'P5.3 xn_1')
set(gcf,'Color','white');
stem([0:N-1], xn_1);
xlabel('n'); ylabel('x(n)');
title('xn1 sequence, N=40');  grid on;

%% ------------------------------------------------------
%%                 DFS(k) of xn1 sequence
%% ------------------------------------------------------
figure('NumberTitle', 'off', 'Name', 'P5.3 DFS(k) of xn_1')
set(gcf,'Color','white');
subplot(2,1,1); stem(k, magXk); %axis([-N/2, N/2, -0.5, 50.5]);
xlabel('k'); ylabel('magnitude(k)');
title('DFS magnitude of xn1, N=40');  grid on;
subplot(2,1,2); stem(k, angXk); %axis([-N/2, N/2, -0.5, 50.5]);
xlabel('k'); ylabel('angle(k)');
title('DFS angle of xn1, N=40');  grid on;

% ------------------------------------------
%  2  x2(n)=5sin(0.1pi*n)   n=[0:19], N=80
% ------------------------------------------
L = 20; n = [0:L-1]; N = 80; k = [-N/2:N/2];            % wave parameters
xn_2 = [5*sin(0.1*pi*n), zeros(1, N-L)];
Xk_2 = dfs(xn_2, N);                                    % DFS
magXk = abs( [Xk_2(N/2+1 : N) Xk_2(1 : N/2+1)] );       % DFS magnitude
angXk = angle([Xk_2(N/2+1 : N) Xk_2(1 : N/2+1)] )/pi;   % DFS angle

figure('NumberTitle', 'off', 'Name', 'P5.3 xn_2')
set(gcf,'Color','white');
stem([0:N-1], xn_2);
xlabel('n'); ylabel('x(n)');
title('xn2 sequence, N=80');  grid on;

%% ------------------------------------------------------
%%                 DFS(k) of xn2 sequence
%% ------------------------------------------------------
figure('NumberTitle', 'off', 'Name', 'P5.3 DFS(k) of xn_2')
set(gcf,'Color','white');
subplot(2,1,1); stem(k, magXk); %axis([-N/2, N/2, -0.5, 50.5]);
xlabel('k'); ylabel('magnitude(k)');
title('DFS magnitude of xn2, N=80');  grid on;
subplot(2,1,2); stem(k, angXk); %axis([-N/2, N/2, -0.5, 50.5]);
xlabel('k'); ylabel('angle(k)');
title('DFS angle of xn2, N=80');  grid on;

　　运行结果：

这两个序列的基本周期不同，但是二者非零元素值相同。x2（n）相当于在x1的末尾进行补零操作，加了40个零。