《DSP using MATLAB》Problem 2.20

Posted 2020-10-17 沧海一粟

代码：

%% ------------------------------------------------------------------------
%%            Output Info about this m-file
fprintf(\'\\n***********************************************************\\n\');
fprintf(\'        <DSP using MATLAB> Problem 2.20 \\n\\n\');

banner();
%% ------------------------------------------------------------------------

b = [1, -1]; a = [1];


%% -------------------------------------------------
%%           3 input sequence
%% -------------------------------------------------
n1 = [0:30];
x1 = 5 * (stepseq(0, 0, 30) - stepseq(20, 0, 30));

n2 = [-1:30];
x2 = n2 .* (stepseq(0, -1, 30)-stepseq(10, -1, 30)) + (20-n2) .* (stepseq(10, -1, 30)-stepseq(20, -1, 30));

n3= [-1:110];
x3 = sin(pi*n3/25) .* (stepseq(0, -1, 110)-stepseq(100, -1, 110));


%% ------------------------------------------------
%%            3 output sequence
%% ------------------------------------------------
y1 = filter(b, a, x1);
y2 = filter(b, a, x2);
y3 = filter(b, a, x3);


figure(\'NumberTitle\', \'off\', \'Name\', \'Problem 2.20\')
set(gcf,\'Color\',[1,1,1])                  % 改变坐标外围背景颜色

subplot(2,1,1); stem(n1, x1); title(\'x1\');
xlabel(\'n\'); ylabel(\'x1(n)\') ;
grid on
subplot(2,1,2); stem(n1, y1); title(\'y1\');
xlabel(\'n\'); ylabel(\'y1(n)\');
grid on;

figure(\'NumberTitle\', \'off\', \'Name\', \'Problem 2.20\')
set(gcf,\'Color\',[1,1,1])                  % 改变坐标外围背景颜色

subplot(2,1,1); stem(n2, x2); title(\'x2\');
xlabel(\'n\'); ylabel(\'x2(n)\') ;
grid on
subplot(2,1,2); stem(n2, y2); title(\'y2\');
xlabel(\'n\'); ylabel(\'y2(n)\');
grid on;

figure(\'NumberTitle\', \'off\', \'Name\', \'Problem 2.20\')
set(gcf,\'Color\',[1,1,1])                  % 改变坐标外围背景颜色

subplot(2,1,1); stem(n3, x3); title(\'x3\');
xlabel(\'n\'); ylabel(\'x3(n)\') ;
grid on
subplot(2,1,2); stem(n3, y3); title(\'y3\');
xlabel(\'n\'); ylabel(\'y3(n)\');
grid on;

%% ---------------------------------------------
%%       stability
%% ---------------------------------------------
x4 = impseq(0, 0, 10);
y4 = filter(b, a, x4);

fprintf(\'\\nsum(abs(h)) = %f \\n\', sum(abs(y4)));

figure(\'NumberTitle\', \'off\', \'Name\', \'Problem 2.20 Zero-Pole\')
set(gcf,\'Color\',[1,1,1])                  % 改变坐标外围背景颜色
pzmap(b, a);

z = roots(a); magz = abs(z)

　　运行结果：

        上图看出，三角波信号的微分结果是方波。正弦信号的微分当然就是余弦信号了，见下图：

        微分器的脉冲响应序列是绝对可和的，所以系统是稳定的。