Find some problems need to be discussed

## Problem 1.4

### Question a

### Task a

![](P1_4_a_out.png)

As shown in the figure, $x_1[n] = \delta[n]$, $x_2 = 2\delta[n]$, $y_1 $

stem(n,y1);

title('1.4 (a)-1');

xlabel('n');

ylabel('y_1=sin(\pi/2) x_1[n]');

ylabel('y_1=sin((\pi/2) x_1[n])');

subplot(2,1,2);

stem(n,y2,'r');

title('1.4(a)-2');

xlabel('n');

ylabel('y_2=sin(\pi/2) x_2[n]');

ylabel('y_2=sin((\pi/2) x_2[n])');

saveas(gcf, "LAB1/P1_4_a_out.png")

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%不满足稳定性、可逆性

% Stability, invertability not satified

%（y趋近于无穷，不符合稳定性要求）

% Stability, causality analysis

% Stability, causality analysis (y趋近于无穷，不符合稳定性要求）

%可逆性分析(两个不同的x得到了相同的y，不满足可逆性)

n=-5:1:5;

x1=n;

y1=n.*x1;

xlabel('x1');

ylabel('y1');

%可逆性分析(两个不同的x得到了相同的y，不满足可逆性)

% 时间无关性分析

% time-invariant

x2=[zeros(1,5) 1 zeros(1,5)];

x3=5*[zeros(1,5) 1 zeros(1,5)];

y2=n.*x2;

y3=n.*x3;

y3=(n+1).*x2

subplot(3,1,2);

stem(n,y2,'r--h');

xlabel('x3');

ylabel('y3');

% 时间无关性分析

% time-invariant

saveas(gcf, "LAB1/P1_4_f_out2.png")

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